The following info is based on my limited knowledge of this island. My advice to you is to actually get a guidebook to help you decide on what you would like to do once you get here. We have a bunch (if you are coming to visit us) or if you just like to pre-plan, here are the books I've found most helpful.
Genki Sushi - they are everywhere; one of the cheap sushi places on the island. What makes this place fun is that all the tables are set around a huge conveyor belt, on which there is an endless parade of different kinds of sushi. Just grab whatever you want as it goes by! Fun. (Various)
Taco Del Mar - I'm pretty sure this is a chain, but it has cheap food, and is a step up from The Bell. It is right in Kapolei, where we live. (Kapolei)
The Shack - If you are over by Kailua and are craving a great burger and fries, this is the local place to go. It has indoor and lanai seating, as well as a few video games to distract a hungry guy, if needed. *UPDATE* I recently went back to The Shack, and management must have changed or something, because it was really not good. It's like Wendy's value menu burgers, except expensive and you have to tip. So if you are reading an old guidebook, or it gets recommended to you, just say no to crappy food. (Kailua)
Maui Taco - you have to get a burrito here if you are over in Kailua. It's a famous local staple. (Kailua) 
Across the street from Maui Taco is Amina Pizzeria, and they have the most ridiculously good calzones anywhere. They are huge, so splitting with a friend is an economic possibility. Or you can be like me and snork the whole thing down yourself after a long day at the beach. (Kailua)
Matsumoto Shaved Ice - ok, so this isn't really food, per say. However, no trip to the North Shore is complete without one of their great shaved ice. There is almost always a bit of a line, but worth the wait. You can get it plain and boring (like me) or with beans (?!) and sweet cream, if you are being adventurous. (North Shore)
If you like Thai, hit up Haleiwa Eats. It's in the cute little pastel building next to Matsumoto's. It's a small place with indoor dining as well as a patio if you wanna be outside. The food is delicious and very fresh. To get to their bathroom, you have to actually walk through the tiny kitchen and between the chefs, so you get to see them cooking your meal. We've only been here once but sampled quite a few menu items and liked everything. (North Shore)
Shabu Shabu House - This restaurant was named for the type of cooking it uses, and it is one of those things that is unique to the culture that transplanted here, although David took a lot of the fun out of it by calling it "Chinese fondue". I am generally the only haole in the place, but everyone is very polite. Go in and sit down in front of a personal water-filled wok and order your meat choice. I recommend the beef/pork mix. They bring out a tray of thinly sliced, nice raw meat, and your vegetables - cabbage, spinach (?), tofu, Chinese sweet potato, udon noodles and rice. You basically cook your food in the wok and try them in all the different sauces available. It's fun, healthy, and can take a while if you are in a talking mood. It's called Shabu Shabu, because they say that is the sound the water makes when you swish your food in it. There is another shabu shabu restaurant right down the street that has a much nicer ambiance, called . I am not sure what the price range is, however. (Ala Moana area, between downtown and Waikiki)
If you are up the coast in the Waianae area, Makaha Valley Country Club is a great place for a fish sandwich. We came in straight from the beach. Good views of the golf course. Turn mauka (towards the mountains) on Makaha Valley Rd. (Makaha)
Indigo - This is a snazzy downtown bar that has great specials Tues - Fri: happy hour has free appetizers that are pretty fancy for being free. The cost of the martini is definitely worth it. There are several art galleries around the corner if you are feeling so inclined (and more opinionated) after drinks. (Downtown)
The Yard House - A Waikiki joint, this place will have tons of visitors. It is in a tourist-central part of town, which means it is a nice and fun area. This restaurnat is famous for its 100+ beers on tap. They have great food and great mixed drinks as well, although they are a little pricey ($9). Great place for hanging out and enjoying some tasty American-Hawaiian fusion food and beers.
Lulu's Waikiki - This is a great place for visitors - the food is varied and wonderful, and it is right on the Waikiki strip. The whole restaurant is on the 2nd story, and has no walls to speak of - you have a great 360 degree view of Waikiki, the ocean, and Diamondhead. However, the dinner menu is far superior to lunch, so I recommend coming here in the evening. Hard to spot, and virtually no parking (like everywhere else downtown). (Waikiki)
A random pic of the place I got off the internet.
The Olive Tree Cafe - It's been a long time since we've gone here (last time was the day we got engaged) but it still deserves a place on the list. It's Greek - fun, authentic, and has a great ambiance that you just don't get when big companies try to do it. Most visitors who come love the experience. Another thing that I love about this place is that you get restaurant-quality food without having to tip. Walk next door for a bubble tea to finish your meal. (Kahala)
Pizza Bob's - a great Italian joint if you are craving some pasta. They also serve pizza, burgers, sandwiches and salads. Generous portions, and flavorful combinations. It's almost like a mainland joint. (Which is a compliment). (North Shore)
Epic - David has been to this place for lunch and loved it. I'll have to have him guest blog for this listing.
Kuhio Sushi - We frequent this place a fair amount, as it is close to us and offers some decently priced (And tasting) sushi. Decent ambiance, in an outlet shopping center in Waikele. (Waikele)
Expensive ($20 and up):
Roy's (in Ko Olina) - this is convenient, because it is a nice restaurant about 2 minutes from our house. The menu is your traditional Hawaiian fusion, with the lunch menu being significantly cheaper, around $13. The decor itself is pretty ordinary, so if you are going for spectacular, this might not be the place for you. The food, however, is first rate. I got the 'Surf and Turf' and I can honestly say I haven't had food that good in a long time. The steak was cooked perfectly, and whatever that was on my plate around it was fantastic. David's fish was cooked very well too. The desserts are a bit of a let down - typical and uninspired - not bad, just ordinary. I would pass on sweets here. (Kapolei)
The Orchid Room - a nice place, great ambiance, and wonderful views, but I was less than impressed by my main dish. This is basically a steak and seafood house. I'd go here for some drinks and pupus, but go somewhere else if you want to have a special meal while you are here. (Waikiki)
The following are places I haven't been, but have heard good things about (of course they are all downtown):
Oceanarium - So, this hasn't got the best reviews ever, but it has a good lunch menu, consisting of seafood, burgers, steak, chicken and salads - supposedly. What makes this place note-worthy is the amazing 3 story aquarium wall in the middle of the restaurant, complete with a few sharks. Supposedly if it is a special occasion they will drop a sign down in it with 'Happy Birthday' or whatever you like written on it. They send a scuba diver in for feedings at noon and one. (Waikiki area)
Top of Waikiki - revolving steak house in Waikiki that has amazing 360 degree views. (Waikiki. Duh.)
Hanohano Room - also a steak house/Hawaiian fusion with good views of the ocean. (Waikiki)
Alan Wong's - I'm not sure about the view, but the food is supposed to be amazing. Sushi, seafood, and steak. Call for a reservation well in advance, maybe even before you get here if there is a certain day you wish to eat here. (Waikiki)
I haven't been here yet, but it is listed in all the guidebooks as a great beach, so I thought it should get a spot.
I recently finally made it over to the side whrer this beach is, and honestly, I was pretty underwhelmed. Kind of dirty with cloudy water. Blah. If you are going to travel this far, go to La'ie Beach instead - nicer, whith crazy waves, if you're into boogie boarding.
This is a great beach on the North Coast, although it is very different depending on what time of year you are here. My favorite time is in the summer, when the bay is calm, has great views, and pretty good snorkeling around. Also, there is this giant boulder you can jump off of into the water. In the winter, it is a nice beach to look at - which is all you'll be doing. At most of the North Shore beaches in the winter the waves are to big to get in the water safely. It is fun to look at the huge waves though, and in December there are surfing competitions to go watch.
4. Sunset Beach
We live here, so more than likely you are going to visit one of the coves. There are four man-made crescent beaches, all with beautiful scenery. If you have kids, this is the perfect place to introduce them into the water. However, they are always packed, so serenity won't be found here. There are also 2 off-property coves that aren't nearly as crowded, and are more picturesque to me. 
The cove off of the Marriott Beachcomber has a great beach restaurant.8. Pokai Bay
9. * Hanauma Bay
The absolute best place for snorkeling - it is actually a volcanic crater. Now it is a marine sanctuary, and as such has large numbers of schooling fish and other creatures. Surprisingly, this is one place I don't see that many turtles, although you will see them everywhere else. It's very picturesque and always amazingly crowded, although that won't matter as much once you're in the water. There is an admission fee of $5 per person - David and I can get in for free since we're locals, so don't let that deter you.
10. Waikiki
One of those places you just have to go to say you've been there. I actually suggest not even getting in the water, unless you really want to. Waikiki beach is great for people-watching, as it is always packed solid. You can also easily rent surfboards to try your hand at surfing as well. However, usually a lot of people have the same idea, so it is kind of tricky to figure out how to surf and not decapitate people at the same time. I would recommend planning a downtown-area trip, with Waikiki just being a stop along the way.
11. * Lanikai
12. Shark's Cove
This and Three Tables are both popular beaches for snorkeling that are very close to one another. Shark's Cove is for snorkeling only - I greatly suggest that you wear some kind of aqua-booty here. You basically have to climb down boulders to the water, and then across slimy boulders to open water. The snorkeling itself is great - which is why so many people brave the entry. There are many caves and underwater arches around here, so I would recommend diving it if you get a chance.
13. Three Tables
14. Papailoa or 'Lost' Beach
The 'Lost' Set
The unfinished Church
This is a nice picturesque beach, not unlike many others on the island - although it is pretty vacant most of the time. You will see lots of beached turtles, hanging out and getting sun. What makes this beach fun is that is the set for 'Lost'. Along the shoreline there is the beach camp, the church (that never got built) and a few other sets that I have no idea what they are. I say it is one of those Dharma-bunkhouses, but David thinks it's nothing. You can't really investigate, because there are guards watching you in the background. But it's fun to see in real life what you watch through the TV screen each week. So this beach is basically for the Lost-junkies and those wanting some solitude.
*UPDATE*
I recently went back to this beach, and the Lost set is gone. There is still the roped-off area, but the actual props have been taken away, and the church has been dismantled. I'm not sure if they were only up previously due to the writer's strike or what, but it is no longer available.
15. Electric Beach (Kahe Point)
While this isn't a pretty beach, the snorkeling here is phenomenal - as evidenced by the charter boats always anchored nearby. It is called Electric beach, because it is right by a power plant that releases steam into the ocean, causing it to be a little warmer, and for the ocean flora and fauna flock to the area. The beach itself isn't crowded, but there is a steady stream of snorkelers and divers getting into/out of the water. It is also right next to where we live, so you won't have to drive very far.
This place is kind of pricey, at a $85 price tag per person. However, it is an all-day activity, and includes a luau that evening. I believe it might regularly be a bit more (closer to $120?) but the kamaina (local) discount reigns supreme. This place is kind of like the Six Flags Over Texas of Hawaii. There are basically (I think it actually is six) different areas of the park, and they are for the different island groupings of the Pacific - Hawaii, New Zealand, Tahiti, etc. Each area has demonstrations, activities, and food that is unique to their area. We did such things as hula dancing, spear throwing, and a bunch of other things I don’t know the proper name for. Midday there is a big floating parade on the river running through the park of each island's local dress and dances. Also, we went to an amazing fire dancing show in the evening after the luau. The luau itself was mildly bland, but then again, I'm not too excited about luaus. Once you have been to one, you're set. Although, after some research I figured out it's rated the best luau in the islands, and it's a great price too. The regular price tag for just a luau dinner is around $60. Anyway, it is a fun way to really get some culture of the islands.
This isn't a very big park, but at the same time it is very beautiful. If you have ever seen '50 First Dates' you've seen the place - it is where Adam Sandler works. The highlight is the dolphin show, and the small crowds that allow you to get up close to the animals. A fun way to spend a few hours, on a beautiful location. Admission is $29/adult. http://www.sealifeparkhawaii.com/
I haven't actually been to these, but if local flora is your thing, I've read that the gardens are very beautiful. I think admission is actually free, as well.
In all honesty, I was underwhelmed by my visit here. I basically went because it was on the way to the North Shore, and it is one of those touristy things you 'have to do'. While the ride in used to be very picturesque with the fields of pineapples stretching into the distance, now the actual farm has been closed, leaving bare fields to greet you. The plantation itself is actually just one big store where you can buy pineapple-related things and foods. We browsed quickly through the store, got some pineapple-flavored soft serve, and went out back to look at the examples of different kinds of pineapples in a small garden. I believe there is a train ride available, but we decided to skip it. Buy your pineapples elsewhere - there is a bit of a price hike at Dole. 
we haven't done any chartered boat dives yet - so I don't have a company to recommend to you. On average, it will cost around $90 per person to dive.
if you ever find yourself wandering around downtown, Chinatown is always a fun place to go to soak up some culture. It is mainly food markets, but I enjoy wandering the area and looking at a whole new direction of commerce.
This is located downtown by Waikiki, and it is a well put together exhibit. There are many displays, and you get a personal tour guide recorded thing at the front. They have a large indoor area for all the fish, and then a smaller outdoor area featuring monk seals and mollusks. Great chance to see lots of native varieties of fish without actually getting wet. It took us around 1 1-1/2 hours to get all the way through it. $7 admission.
