You don't see a lot of sharks off Grand Cayman and there's no shark feeding dives like they have some places like the Bahamas. But there's Stingray City where they feed the stingrays which is a fun dive. And there's lots of good diving excursions to reefs, walls, and night dives.
You can dive from the shore at a few hotels but not most places (including the Westin.) Only a few hotels have dive boats dock right there (also not the Westin.) I don't know if any boats pick up on the beach at the Westin, but if not there are many dive operators and they will all pick you up and take you to their boat where ever it is docked.
The Westin is nice, what kinds of things it has to do I don't remember as I only went there for dinner. I'm sure someone will chime in soon with any other ideas on good "family" resorts. There are also lots of condos for rent on 7 mile beach where you would have a kitchen and more space, but maybe fewer "activities." It depends what you want to do when you get done diving. Some of the things you might want to do are scattered around, so for it those doesn't matter too much where you stay anyway.
