My family went to Hawaii again this past June, but we only stayed on Waikiki/Oahu. Your daughter will probably enjoy the Honolulu Zoo, although it's quite fun for everyone. You should also try going to the north of the island and all of the famous beaches, though you should get there early. Otherwise you'll either not be able to find a parking spot or you'll have to walk a ways to get to the beaches. Also, climb Diamondhead. It's a great view once you get to the top, although it is quite a hike to the top. I don't know if you or your family are up for it. Also, you may get to see the giant waves, maybe even the famous surfers who ride them.
We went to an awesome snorkeling spot, I think it was Wayamea Bay (sp?)? I can't remember for sure, but it's the crater where you have to get there early before all the parking spots fill up. The best way to get there is to take the city bus there, it's much less of a hassle, although they stop going there after a certain time so you have to watch the time.
Restaurants on Oahu. There's a place next to the Honolulu Zoo called Teddy's Better Burgers. Eat there. Best burgers and shakes I think I've ever eaten. Another great restaurant on Oahu is Keo's, it's supposed to be world famous so you might have heard of it. Thai food. Good stuff, and awesome service. Our waiter's name was Hal I think, so ask for him if you like to laugh. And then there's always Duke's Canoe Club which has pretty good food as well.
Have fun, hopefully some of this advice will pay off for you.
