jeffreyt is probably referring to La Mer. I like Nicholas Nickolas; its on Atkinson near the Ala Moana shopping center. Also, John Dominis for seafood (excellent Sunday brunch).

I highly recommend the Diamond Head hike (real easy and great view) and Hanauma Beach Park.

If you're interested in Polynesian culture, the dinner show at the Polynesian Cultural Center is done well. The dinner itself (Luau) is okay; basic "hawaiian" foods with some Western (just in case you find that you don't like the hawaiian stuff). If you have the whole day to spend, you can take part in games and crafts from the various cultures.