I've kited in Nassau and St Martin,
i'll start with Nassau. there are 2 places both quick and easy from the ship. check them out on Google earth.
Cabbage beach - on paradise island, ask the taxi driver to take you to the public access area near the golf course end of the beach. (they will probably pretend they don't know where it is cause its quicker and easier for them to drop you at the hotel end of the beach and they are more likely to get in the line to pick up a fair for the way back. ) but if they do drop you at the hotel end its not the end of the world just means you need to walk an extra 10 mins up the beach to get away from the crowds a bit. you will always find a taxi going back to the ship at the hotel end of the beach. so best to make your way there at the end of the session. best for north east winds. think its bout $5-$10 in the cab.
Cable beach - opposite cable golf course. (very close to the ship) but only works with north or north west wind. jump in a cab or local bus few minutes down the road.
for any wind with south in it i think you will be able to kite at south beach but I've never been there. If you go let me know how it is.
St Martin - yea your right best bet is Orient bay, there is a kite school there, you need to kite out in the bay because the beach has a swimming zone and is crowded, but there is a launch and land channel for the kiters to go out and come in. to get there just go to the bus station in the port where everyone is heading like cattle and get the shared bus/taxi there. they will be leaving all the time and its not a problem getting there or getting back.
The other option might be Le Gallion (if people are still allowed to kite there, this has been a long standing debate so i'm not sure on the latest info, haven't been there for a while). its right next to orient bay much quieter, super flat water, but launch and land is a bit trickier most people launch in the grass area car park then walk past the trees to the beach. lots of glass around the car park so be careful of your kite and your feet. Just stay away from the populated are of the beach next to the cafe. Again you can get a shared taxi and they will drop you here en-route to orient but you might pay a bit more cause the road is really shitty and its a little out the way (they don't like going down it in the car.)
St Thomas, I never found a good option here cause i haven't been too often and had limited time, but i suggest find a beach on Google earth on each side of the island then just check the wind that morning rent a car and drive to the best beach. Most of the time you can figure out if its suitable beach by looking at all the pictures people post on Panaramio.
study the areas closely on Google Earth its awesome for figuring out where to kite.