We have been to Hawaii several times. The last just 2 years abo this month. Our favorite island is the Big Island of Hawaii. Kaui is a close second followed by Maui, and lastly, Oahu. Definitly see more than Oahu. The long flight makes a longer trip necessary, in my book. I no longer go to Hawaii for less than 3 weeks at a time, and I only fly first class when I go there. It's just too long a flight, and my arthritis doesn't like siting in coach that long.
Oahu has so many historic places that are not to be missed, including not only the Arizona, but also the Bowfin, The Palace, and a wonderful museum that can take most of a day all by itself! It's also great to drive around the island and go to the north shore and see the surfers (in the right season) and the Polynesian Cultural Center.
Maui has lots of great sights, but is a bit commercial, so some of the charm that it used to have is now lost. Kaanapali Beach area north of Lahaina is the best place to stay here, and Haleakala crater and the road to Hana are not to be missed. If you are there from January to May, whale viewing boats are also good. It is also a great place to golf.
Hawaii (our personal favorite) retains a lot of the old Hawaiian culture, and has so much variety! The north side is where the huge Parker Ranch is, along with the beautiful town of Waimea (SP?). The Kohala coast is possiblly the best sunset watching anywhere! Volcanos National park is wonderful, and taking a flight in a helicopter or small plane around the active volcano is a must! The eastern side of the island has the most gorgeous water falls and lava coasta areas. Hilo is the flower capital of Hawaii and can be very quaint. Our prefered place to stay on Hawaii, is the Kailua/Kona area because it is central enough to make driving to the other areas easy, and there is a LOT of Polynesian history in that area, not to mention all the coffee plantations!
Kauai is also very old Hawaian, and has an ordinance against high rise buildings, so you can still see the beauty. It is called the Garden Isl, because it is the oldest and thus more green. Wildlife here is amazing, and there is great diversity in the weather on the various sides of the island. You can go from Wiamea Canyon with lots of rain and lush valleys to a desert at the bottom! We prefer staying on the north side of this island, in Princeville or Hanalei. Hiking is really fun here too!
Have a fun trip!