Aloha! I just saw this (haven't been on the boards in a while) and I currently live on Oahu.
Waikiki Beach is nice but can get very crowded. Ala Moana beach park is nice (and is right across the street from the Ala Moana center, the big open air mall which I love...maybe because it has a
Disney store 
) The Ko'olina lagoons are very peaceful and quiet and Aulani is beautiful. Kailua beach park is nice from what I hear but I usually frequent the beaches on MCBH. (Marine Corps Base Hawaii) Turtle Beach, like somebody else mentioned..you will see a lot of turtles but make sure not to touch them and keep your distance. (It's a state law.) You may also see Hawaiian monk seals on some beaches but they are protected under the same law as the turtles.
The Honolulu Zoo is one of our favorite places to visit with the kids! Dole Planation is nice and you can grab a dole whip there.

It can get crowded quickly there, though..just like everywhere else.

The train ride there is nice but can be a long wait.
If you are looking for a place to get out of the heat, there is an ice skating rink near Aloha stadium. (Yes..ice skating in Hawaii! My oldest dd takes lessons there)
Pearl Harbor is a must but be prepared to not carry any bags in. We did Pearl Harbor when we first moved here with a 1 yr old, 2 yr old and 3 yr old. Rimpac will be going on next month so the base will be quite busy..however the USS Arizona Memorial (among other sights in the PH area) are not on the base.
Most restaurants out here are kid friendly.

And some must haves to pack..definitely sunscreen, sunglasses, bathing suits, flip flops (they call them slippers here), "summer" clothes and an umbrella if you can fit it.
There is more I can think of but feel like I've written a book so I will stop for now.
