Rent a car, drive up to the North Shore and watch the real surfers up there. You can find some nice out of the way restaurants up there also. While in Waikiki, go parasailing. About a mile off shore, 250 feet in the air, just gliding around - beautiful views of Waikiki Beach and Diamond Head. Probably around $50 a person for a 30 minute or so ride, but so worth it. Try to take in one of the traditional style luaus also - the Kalua Pork is some of the best pig you will ever eat. Taste the poi just to say you did it, but don't expect much. It tastes like purple paste.
A tour of the Dole Pineapple Factory is also nice, then try the pineapple soft serve before you leave the facility. While you have the car rented, just drive around the entire island of Oahu (takes about 3 hours or so, depending on how many stops you make). If you like pics, stop at the blow hole around Hanauma Bay, and make sure you get to see Chinaman's Hat. As mentioned previously, take the Diamond Head hike - make sure you wear comfortable, closed shoes, take a couple bottles of water with you, and ensure you have your camera with you.
Oh, and if you have any sense of pride in your country, the Arizona Memorial is an absolute must.