We have gone to Hawaii, - Kona (big Island) three times, Oahu three times, Maui twice, Kaui once and Molaki (sp) all with our kids. They are now three yrs and 14 months. We liked staying at the condos on the big island (Kona). You can find some on www.redweek.com and sign up to see the weekly rentals. We stayed up north at the Hilton Village and the Hilton Grand Vacation Club (awesome condos) at Waikoloa. The condos have washer dryers and full kitchens so you don't have to eat out all the time.
I personally think that the big island is the best for families. There is a lot to do on the island as far as sight seeing or if you just want to hang out at the beach there is a great public beach right by the Marriott resort, north of Kona at Waikoloa.
What ever you choose have a great time. We just got back from Kona last week and had a great time.