You'll be find going on your own for St. Thomas and Grand Turk.
As for Nassau - to be honest I stay aboard these days while there but you can go out to Cable Beach and buy a day pass at the casino hotels, or just head over to Paradise Island and check out Atlantis. That can get expensive though, but you can do some things there and not burn a whole in your wallet.
San Juan - depends on when your ship is in port. Are you there in the daytime or is it into the evening?