I've made the trip a few times around the west end of Cuba. It's nice to follow the Keys and Dry Tortugas. The current is not too bad, except for off the west coast of Cuba where it can get up to 3 or 4 knots from the south out in the middle of the Yucatan channel. If you stay within 15 miles (but at least 12) of Cuba, the current won't be bad. Along Florida and the keys it's pretty easy to stay out of the Gulf Stream by keeping close to shore.
If you go the east route around Cuba, you can visit a lot of the less busy Bahamas. I personally would stay clear of Haiti because of the lack of law and order, although other people do sail there and most come back alive.
You could check the pilot charts (
Maritime Safety Information) for the month of your trip, but most of the trips I've made between Florida and Cayman had fairly light wind.