There are a series of books with good info on what to do on the islands. My parents bought Maui Revealed and Oahu revealed when they came to visit us. So I guess its the (insert island name here) "Revealed" books. They have a lot of good info on where to eat, less touristy yet very cool things to see, best beaches, best shows, best luaus etc.
While on Kauai go to Polehale Beach if you can get there. It's worth the extra effort of getting out there. I'd rent a jeep or some kind of SUV for this. Just dont tell the retal car company that you're going there. Also try Koloa Landing for both shore diving and snorkeling for the rest of the family. Its a really easy entry and most dive ops go there, but you dont need one if you're comfortable with shore diving on your own.
Check out Fathom Five dive op on Kauai.
A trip to Ni'ihau is cool too. You can take one of those charters out there and they let everyone snorkel, plus feed you and let you drink. We went with Blue Dolphin charters when we did it and for an extra $25 we got to dive instead of snorkel, and to this day it's still undoubtedly the best dive I have ever done.
Check out Oki Diner in Lihue for some tasty ono grinds. The food there is awesome. Pancakes for breakfast and Neils Favorite chicken for lunch. Everything we tried there was awesome.
On Oahu...
The Aloha Market at the stadium is pretty cool, its a great place to get all your Hawaii gifts for friends and family back home. Lots of souvenir stuff as well as really tasty Hawaiian jams and sauces.
Go to Hale'iwa on the North Shore, it's a neat little town, great diving very near by (Shark's Cove, Three Tables, The Trench, etc). Also the Dole plantation is on the way up there. I have never been, but there are always a lot of people there, so my guess is it might be worth checking out.
Also Sea Life park on the East side of the island is a good family activity. My guess is it's like Sea World, but Hawaiian Style. I hear it's a nice place.
The aquarium in Waikiki is worth checking out, its pretty neat and I think tickets are only $9 for non residents. The zoo is right there as well, but I have never been so I have no idea what its like.
Waikiki is way over rated by the way, spend more time other places. The beach there is crappy and really rocky and really really busy. Even if you head closer to Diamondhead there are less people and the beach is a bit nicer. I don't know why Waikiki is as popular as it is, it's really not worth it.
Check out Big City Diner on Oahu. There is one in Kaimuki and also one at the Ward Center. Good for local style food or even a great cheeseburger.
Hope that helps...