Some of my family live on Oahu. There is plenty to do on the island of Oahu, just get out of the city. Everytime we go the only time we go toward the city is either to go to the airport, the flea market or Pearl Harbor. Get away from the city. Go stay on the windward side or toward the north shore, the beaches are less crowded and you'll have a lot better idea of Hawaii afterward. Hanauma bay is a nice place to snorkel, but get there early before it gets really busy. The Polynesian Cultural Center would be a good place to go also.
Drive the highway along the coast from the windward side of the island from Hanauma all the way up to the North shore and into Haleiwa. Along this route you will see several different beaches to stop at, check out some good local food, and shopping. You could spend days doing all the things to do in those areas. From Haleiwa you can take the highway back toward the center of the island and hit the Dole plantation. A few of my favorite local places to eat are Keneke's in Waimanalo (Keneke's looks a little scary from the outside, but trust me. try the Kalua <sp?> pig plate), Buzz' in Kailua (right accross from Kailua beach very nice), and Haleiwa Joe's in Haleiwa.
These are just a few of many things to do on the island. But these will give a better impression of the island than only staying in the city. If you only stay in the city you will miss out on so much. Just remember to be respectful of the locals.