I think you really will want to rent a car there -- exploring the island is the best part! And if you go to the Pearl Harbor Memorial, it is a bit of a ways from Waikiki, so a car would be good for that, too. I would recommend renting a car at the airport -- the in-town car rentals tend to be more expensive and can close on the early side (so if you are exploring and get back late you can get dinged for an extra day).

Another recommendation is a stop at the Hanauma Bay Nature Preserve -- beautiful beach and phenomenal snorkeling. You can rent snorkeling gear and a locker on the premises. The only drag is you have to sit through a short film on the environment but it goes by quickly and isn't too tedious. It truly is a beautiful spot!