I have not stayed at any Starwood properties in Hawaii, but Maui is a great island to visit.
As for the Caribbean, I've been to all three Westins: Puerto Rico, Cayman, and St. John. Depends on what you're looking for. The Westin Rio Mar in Puerto Rico would seem to be a great place for a family vacation. It has lots of activities and amenities, and a rain forest a 20 minute drive away.
St. John is a great island but the Westin gets mediocre marks for service. Still, a nice family destination with gorgeous beaches and scenery, although very quiet at night.
Grand Cayman is a nice resort but isn't very large in that it doesn't have acres of resort grounds. It's bordered by one of the main drags in Cayman. It feels more like a nice hotel on the beach. On a great beach, and the island itself is very upscale, but lacks the gorgeous scenery of St. John. If you like watersports, Cayman is terrific, as is St. John. Puerto Rico not as good but it is there if you make more of an effort to access it.
If you're really into snorkeling or scuba, I'd recommend either Cayman or St. John. If you just want to do a variety of family activities, then Puerto Rico may be your best bet.
Feel free to email me if you want more information.