A Caribbean Cruise is an excellent suggestion. However, if you intend to be land based, Ft Lauderdale, Florida is magnificent. It has a very nice beach and some great hotels on and off the beach. The ones with beach access will be pricey. But there are smaller ones within walking distance to the beach which can be had for good prices. There are some very nice and lesser known areas to the north with nice beaches as well, Pompano Beach (north of Ft. Lauderdale) North Ft. Lauderdale - has some small motels on the beach which are not that costly. Miami Beach is also a very nice wide beach and most of the beaches are very good for kids as they slope gently out to deeper water. Pay attention to the life guard warnings posted (for things like jelly fish, rip tides etc. Not frequent but they are good at monitoring what is going on in the water and on the beach.) about 10 years ago
Disneyland in Anaheim is a must do with kids and if the kids are older maybe Knotts Berry Farm. Universal Studios is also good for kids.
In Australia we have plenty of things to do. In Queensland there is a water part - Wet 'n' Wild, Theme parks which are Dreamworld which has rides and animals (tigers), White Water World which is right next door to Dreamworld, Movie World is another theme park. Most of the Hotels in Queensland have pools. If you base yourself in the Gold Coast you can travel up the coast to Noosa and the Sunshine Coast.
There is also the Australia Zoo, Big Pineapple and much much more to do in Queensland. There are plenty of islands off Queensland at stay at some are Hamilton Island, Day Dream Island, Lizard Island and many more. about 10 years ago