In ST. Thomas there is "Little Magens Bay Beach" it is right next to "Magens Bay Beach" however taxi drivers don't like to drive you there and you need to walk down the mountain to get there. If you are looking at the water from Magens Beach walk all the way to the right and walk along the rocks in the shallow water. Little Magens Beach is on that right side , about 20 minute walk.
I am unfamiliar with another beach called Linquest Beach on St. Thomas, however I have been told it has some nude use. I have not been there and I do not see it listed in my World Guide to Nude Beaches.
I have never been to ST. Croix and do not have information on it in my guide.
Matthew, you are absolutely correct, my ex-wife lived on St. Thomas for 7 years and I remember her telling me about that little beach, but I also recall her saying that on some occasions the authorites would come around, it is after all not legal in the USVI.
Any of the French islands it's legal.