We have been to Grand Cayman, Grand Turk , Curacao, and just returned from Cozumel last week. All these destinations are top dive destinations in my opinion. I concur with Dennis 49 for Ambergris Caye, especially if you desire family-safe enviornment, with absolutely great diving. We stayed at Ramon's, a solid standard for the island, with beaches, pool, great diving operation, and convenient to the island fare. Grand turk (Speir) is also exceptional for a dive vacation, and definitely look up Smitty for your dive operation.
Curacao has the most to offer if you spend time above the ocean, or have concerns for Hurricane season. Many nice resorts outside of the capital city, ( we stayed with Habitat and Easy Divers, exceptional !), But you may want to rent a car for a few days there.
Cozumel's diving was still the greatest, but the island is now a tourist destination, ruled by the days the cruise ships are in port. Beaches are hard to come by without the big all -inclusive, but the El Cozumeleno is still there, with expansion and improvements. I think you can get direct flights to all the destinations I've listed, but Curacao may need a stop in Aruba.
Good luck planning your trip. Airhead 52