Going to any other Islands? I went to Maui 6 months ago for my honeymoon. It was awesome, but wont be of much help to you on O'ahu. General advice for Hawaii though, make sure check out different beaches. Maui has a pure white, a black, and a red sand beach that were are really cool. Snorkeling is a good idea... all kinds of cool ocean life, sea turtles and shit. There are hikes on Maui that go back to active waterfalls you can swim in. Im sure O'ahu has some similar sites. That was an awesome experience. We drove to the top of a Volcano to check out sunrise early in the morning. Fantastic views.
Most of the best advice we got was by asking locals though. Travel books will give you the crowded touristy things to do that usually cost money. Go to a local bar or restaurant and ask the bartenders and servers. They will generally have the best advice and can give you kind of an inside scoop on what to do.
Edit: Just my 2 cents, but for all the people telling you to stay in your room and have sex... if you married the right girl, you can do that anytime. You can sit in your room in Ohio or wherever you live and get laid any time you want. Get out of the room and enjoy every minute that you can. Hawaii is awesome, and for many, a once in a lifetime experience.