Cozumel in the Mexican Caribbean is always a great choice. Excellent diving, great vis, awesome coral structure, loads of fish, warm water. It's also easy to get to from the US and relatively cheap compared to other areas of the Caribbean. I can't compare the diving to the rest of the Caribbean though since I've only dove Coz and the Mexican Riviera.
Grand Cayman is more expensive and is beautiful, with stellar diving from what I hear - but I didn't get to dive there so can't help with the dive questions.