With only two months, unless you want to sail most of the time, and explore not very much, I would say head for the Bahamas. Central America is going to take you a couple weeks to get there, and could take a lot longer to return. Unless you make each way a non-stop passage, and you would want good offshore experience to do those slogs. The Bahamas can be reached on an overnight crossing, and then you can just island hop for as long as you like, with an easy return. Beautiful water in the Bahamas, too.
The Thorny (or Van Sant's Thornless) Path is a long slog. We left Georgetown in the Bahamas and it took us a week to get to Puerta Plata in the Dominican Republic (though it was in December when the trades are very strong). Working hard you could get to the Virgin Islands easily in two weeks, and the return trip would likely take only 7 to 10 days. But you've got a lot of watchkeeping (the Mona Passage is a very busy place for commercial ships, and the US Coast Guard will visit your boat most likely).
The Dominican Republic itself can be an interesting destination, but for clear water and good diving, I'd vote for the Bahamas.