We went to Oahu on our honeymoon.
Waikiki is obviously fantastic.
We're history buffs, so we spent a morning and early afternoon at Pearl Harbor, which was great. As was said -- get there early. VERY early. We were there at, I believe, 7 a.m., and still had a several hour wait.
We went to an outdoor market in the parking lot of Aloha Stadium, which was a lot more fun than it sounded. We bought all kinds of cool stuff, cheap. And it was fun talking to locals.
Hiked up Diamond Head. That was awesome, and the view from the top is incredible.
The absolute best thing we did though, was something I'd never heard of until we got there. The Polynesian Cultural Center, somewhere on the north of the island. It sounds kinda lame, but it was great. You get to experience life in the different cultures of Polynesia, and there's a kick-ass show at the end of the day. Like I said, sounds lame but it was fantastic.
Also, someone else suggested renting a car. We stayed on Oahu the whole time, and from our hotel, there was shuttle service to absolutely anywhere you could want to go, and a help desk on the main floor to get you reservations. So if you're going to stay on Oahu for an extended time, I actually recommend not renting a car -- it's cheaper and less stressful than renting a car and dealing with the mess of traffic at that place.
Edit: I forgot the pineapples. You have to eat a fresh Hawaiin pineapple. I didn't like pineapples before we went there, tried one and fell in love. And now back in the states, I hate them again. I can never find Hawaiin pineapples here (they're always from Mexico or Peru or someplace), and pineapples from other places just aren't very good. I don't know how to explain it.