Have fun in the Bahamas. I've actually enjoyed my time kiting there more than any other place in the world. I like that it's not really known as a kite destination and most of the islands are untouched. It's really more like adventure kiting as compared to the venues that are packed with tourist kiters.
I've always judged a kite location not by the windy times, but more by what you can do when the wind isn't blowing. Spearing, fishing, and exploring are all great in the Out Islands. Certainly there are more consistently windy locations than the Bahamas, but with new gear including foils, the Bahamas are quickly becoming even more viable as a destination to kite. I'd also say that from October - mid-June, you are very likely to get some great conditions weekly.
The islands are more expensive than many other locations, and certainly life is a bit slower in the more remote regions. One of my favorite locations is in the Northern Berry Islands at a place called Great Harbour Cay. GHC boasts amazing beaches that are positioned to take advantage of the most common wind directions. You can rent a condo on the beach at a reasonable price and you may even see 1-2 kiters during your stay. You are close to blue holes, and there is a remarkable downwind ride over some amazing flats! In truth, it's probably tough to stay there for more than a week or two for most, and this is especially true of you don't freedive, fish, or spearfish. You would be best to bring most of your own food, but there are places to stock up on the island. There are a few places to eat, but options are very limited. I love this island. I'm sure that the wind is a bit better if you get down to South Eleuthera or the Exumas, but having a foil or a surfboard in the Bahamas is your best insurance policy against light air. There are no waves at GHC which is a bummer for sure, but the location is so nice that you probably won't mind.
If waves are a necessity, then I'd probably recommend Great Guana Cay in the Abacos. Most of the outer islands in the Abacos will be find for kiting, but Guanna has a longer stretch of beach than most. It's certainly got more action than GHC and you are very close to several other islands via ferry. You can generally go between Guana, Treasure, Green Turtle, March Harbor, and Elbow by ferry for about $15-$20 for 20-30 minute service. Note that the Abacos can be expensive depending on the time of the season.
Eleuthera is another great Bahamian wave destination. If you want to stay on a budget, there are some great locations around Surfers Beach, but this is a wave only beach, no flat water within walking distance. You can rent small houses on the bluff that are walking distance to the beach (they are remote though!). There are fantastic flat-water locations on Eleuthera, but this island really requires that you have use of a car. I might even suggest staying down at a place called Pineapple Fields. This beach has a fairly protected inside, with nice waves on the outside, but you have to keep a close eye on the barrier rocks! There is a small super market, places to eat, and it's close to the airport. Very nice, but probably a bit more expensive.
For the ultimate flat water trip (probably in the world), look at the Exumas! My favorite is around Staniel Cay, but it's a bit costly. Staniel Cay Yacht club provides a boat with rental of accommodations. Difficult to kite right out of this island, but with the boat you can kite a number of cool spots. Be very careful, as many islands are private and not available to kite on. The Exumas are a world wonder for sure!
Exumas Kite Trip Video-
https://youtu.be/MR_k2zMQ4rc
Crooked Island Kite Trip Video- (pre-hurricane. i'm sure that there isn't much available down there now)
https://youtu.be/2ct_g3ko5Lc
Bimini- Closest spot to Miami. I really enjoy it, but the wind conditions are only a bit better than Miami (very much like the keys).
https://youtu.be/LjJeQfG3NFE
Eleuthera- super old clip with bad quality, but you will get the idea!
https://youtu.be/JYq-DYaNjwg
Exumas-
Crooked Island-
Enjoy your adventure!
Crooked Island- unique kiting exploration
Crooked Island- miles of waves
Bimini (and the rest of the Bahamas- land of the Bulls!)
Enjoy!
Kent