Hi,
Eleuthera ( One of the outer most islands of the Bahamas, close to 160 km long x 1/2 km wide) has heaps of potential. Being one of the outer islands it does get some fun waves, but if you want flat water, take 1/2 km trip across the island, and you have the flat caribbean sea. This island is very remote and isolated ( plan to kite alone), and is not really all that nice to look at...... very scrubby. Water is amazing, like kiting in Gin, incredibly clear. I do believe that nassau has a couple of kite specific camps, a quick google search will turn those up, and they can give you the complete run down on kite sizes, time of year etc. Need to be flexible in the carbi, hurricanes give the place a good flogging each year. Keep an eye on the weather map, and an ear to the weather ready, and have a travel agent on speed dial.
Have also kited in Puerto Rico in the town of Isabella at the N.W. corner. Shacks is a great wave, to surf or kite, friendly kite crew ( usually kited with 6-10 guys), heaps of accommodations that are reasonable ( I would look on craigslist.org..... I found a granny flat to rent out there for a month for 700 USD). Wind was a little touch and go, but that is standard for chasing wind/ waves. La Pargura is a large flat water bay in the S.W., common to see people kiting there. Lots of room.
Both the Bahamas, and P.R. can get a little pricie. I think the dominican would be cheaper, with good wind, but huge crowds.
Know nothing about Cuba.
Hope this helps