Regarding Nassau, there are some reasonable launches off of Hog Island, now called Paradise Island. As always, you will need to walk to avoid the crowds.
There was a guy launching off the east end of the northern shore of Paradise Island when I was there. There is a long sand beach along the shore there.
From:
http://www.tradewindtours.com/
The beaches are signified by the umbrellas.
From:
http://www.bahamatravelnet.com/
So, depending on where and if the wind is blowing from you have other options around the island. There are little lay bys where you can park your car or moped and walk out into the shallows off the east end of the island and do an assisted launch. Normally winds would be from SE to E this time of year if they are on.