Well, as a "born-and-raised" here in Hawaii, and as someone involved in the Tourism industry, this is MY "short" list:
1. Arizona memorial - National Park Memorial to the service members who died on December 7, 1941, They also have the USS Bowfin Submarine museum, the Battleship Missouri, and the Pacific Aviation museum on Ford island.
2. Diamondhead State Park - Hike to the top of the "World famous Diamondhead crater" for a scenic view of the south shore of the Island of Oa'hu, make sure you bring some bottled water with you. It's best to go early so it's cooler than if you go at 12 noon.
3 Bishop Museum - Repository of artifacts not only of Hawai'i, but of the Pacific.
4. Honolulu Academy of Arts (to include the tour of the late Doris Duke Estate at Black Point)
5. Ft. DeRussy Army War Museum (Kalia road) -
5. Circle Island Tour (Haunama Bay. Halona Blow Hole (From Here to Eternity beach Love scene), Makapu'u (And the Light house hike), Lanika'i Beach, Pali Lookout (Can see most of the East coast of the Isaland of O'ahu), Chinaman's Hat (Ku'uloa Ranch), Crouching Lion (near Kahana Bay), Kahuku Shrimp trucks, North Shore (Banzai Pipeline, Sunset Beach, Sharks Cove, Pupuke'a (He'iau), Waimea Bay, Laniloa Beach (where the Honu or Hawaiian Green Sea turtle hand out on the beach), Hale'iwa town, Dole Pineapple Pavillion.
6. I'olani Palace/ King Kamehameha Statue- The only Royal palace in the United States. Did you know that the I'olani Palace had electricity before the White house in Washington D.C.?/ The statue of the King that united the Hawaiian Islands.
7. Kawaiha'o Church/ The Mission Homes Museum (The church the Royalty attended/ where the missionaries lived when they first came to preach christianity to the Hawaiians)
8 The Honolulu Zoo - World class Zoo!
9. Polynesian Cultural Center Tour - Best way to experience a Luau, with walking tours through the villages of seven different Pacific Island cultures, and the grand finale Polynesian Revue show after the Luau.
10 Sea Life Park - Where you can (Pay of course) SWIM with the dolphins and view aquatic life of the Pacific ocean.
That's my "Top ten" list of things to see and do for the FIRST time in Hawaii. (NOT in order of best to worst, just a list of suggestions to see and do while on O'ahu) :P