I am from Kaimuki which is near Kapahulu (which is near Waikiki) on Oahu ...
My suggestions because I am cheap lol:
* Diamond Head - though the hike to the top might be too challenging for a young child. My kids enjoyed climbing trees and ran around in the fields in the crater.
* The Waikiki-Kapahulu Library is a nice place to visit and check out books. All state libraries offer a $10.00 visitor card which is good for 3 months (but may not be renewed) and also a $25.00 non-resident card good for five years and may be renewed for an additional $25.00.
* Pick shells. There is a beach off of Kalaniana'ole Hwy in Hawaii Kai near where Costco is (lol). My parents always take my kids there. It's the beach where they mostly windsurf, jetski, seadoo, boat, canoe, etc. I am drawing a blank on the name, sorry.
* You know, the beaches are not all the same there. Lanikai is sandy white (but it gets polluted a lot), Ala Moana is just right for kids (but parking can be a bear), Waikiki Beach is convenient yet congested, etc.
* I just saw this advertised in the local paper there ...
http://www.fieldtripfriendshawaii.com She offers weekly classes so that might not work out too well, but it sure sounds wonderful.
* The shopping centers and some hotels in Waikiki offer many free classes, entertainment, and exhibits. I know they teach lei making and some have daily hula shows.
* Oh, and just so you know and because I read the newspaper often and keep up with the news... Kama'aina Kids, who often is the company in charge of hotel-based childcare, was found negligent in some (2?) cases where they left children unsupervised at one of their standard daycare centers a few years ago (I think). I can't remember the specifics, but I do recall reading about it. It's just to give you a head's up. You definitely want to check it out before you leave your child in any center there, even at a hotel.
* The Superferry is there now:
http://www.hawaiisuperferry.com It's not necessarily cheaper than air travel, but it is an alternative.
Have fun! We are going back for a visit next summer.
