Pearl harbour, if you're into it in a big way give yourself time. Alot of people go to see the Arizona memorial & then skidaddle out of there but there is tonnes more to see including a decommissioned warship acroos the bridge, a submarine & a few musemns both maritime & aviation. To get the full experience of Pearl Harbour I think you need a half day there if not longer to explore both sides of the harbour. Of course a coach tour of Honolulu is a must, they bring you to the famous war cemetery among other sites & if you were like me, a Hawaii Five O fan, you'll want to visit the famous sites connected with the series.
Outside Honolulu there is a famous sea bathing area where you can snorkle without the expense of a boat trip & a ranch where you can partake in all sort of adventurous activities. On the way to the North shore, on the far end of the island, famous for it surfing competitions & high waves, you'll pass the house where Magnum is filmed, if you're expecting a huge expanse of gardens you'll be in for a shock, oh how the cameras lie. There's a famous cultural village run by the Mormons which is a major attraction. Far as I remember we also visited a great night show there with good food besides the excellent & fun day tour. I think we visited a pineapple plantation/novelty shop. Some of the scenes from the Jurrassic Park films was filmed on Oahu, I think near or on the ranch I mentioned which has that very uunusual scenery of kind of folded looking mountains peculiar to Hawaii. Alot of the filming was done on Maui, due to hurricane disruption they had to film on 2 islands instead of just one which I think was the original intention. Not far from Honolulu there us a beautiful botanical gardens that is worth a visit. Of course a visit to the beach in Oahu is a must & a trip in an outrigger canoe with make it. Some of my memories are a bit vague so you'll probably be able to put more meat on the bones of suggestions I've given. Don't forget to buy a Hawaiian shirt when you're there, if that's what you're in to & try to get in a Lua while you're in Hawaii though the one we went to is on Maui. almost 9 years ago
I think sticking to the more local areas is a better way to experience Oahu...if you're looking for a nice beach, no tourists, try Maili or Waianae on the western side of the island. For a killer workout hike up Koko Head or Diamond Head Mountains (do so before noon as you'll melt during the hike). Pearl Harbour is also a good thing to visit while you're here. By far the best part of the island is North Shore..check out the "Art is..." house where you'll find a yard full of spray painted surf boards in Haleiwa. Right outside of Honolulu there's a forest reserve with some great hiking trails.
Hope this helped! almost 9 years ago