We have toured all of these islands many times both ship tours and on our own. All of these ports are very easy to do on your own. You don't need to pay for a ship's tour unless there is something really special like a catamaran snorkeling tour you definetly must do.
St. Thomas just take a taxi to Maegan's Bay, Sapphire Beach or Coki Beach. Or, taxi to Red Hook for the ferry ride over to St. John. Once there, get a jitney tour of the island and stop for a swim at Trunk Bay. (Now, this is my bad experience.) We took the ferry which we had just missed when we arrived at Red Hook thus an hour wait in the sun. Once at St. John it was overcast and the jitney worked out great as it is covered and showers did occur intermittently. When we got the return ferry, we were going to Charlotte Amalie to do some shopping. Well we are at least half-way out into the open ocean waters and we smell smoke! A engine had quit. Now we are just past the entrance to the harbor at Red Hook. The boat does a 360 degree turn and sails back to St. John! If you don't think I was scared to death, I was. When we reach shore the boat captain and other captains start arguing about us getting on board the next ferry. They finally agreed this boat load of people could get on the next ferry, but it was going to Red Hook and they would not refund the difference in the ticket price. I was just very glad to get back to St. Thomas in time to get back to the ship.
St. Martin; there are van taxi's waiting to take you on tours, to beaches, or where you wish to go just outside the new pier area. Don't waste your time and money on a ship's tour unless you wish to try the America's Cup race. Do a half day of both sides of this island and ask them to leave you at Orient or Dawn Beach and set a return time. Leave plenty of time for shopping in downtown Phillipsburg. Everythings Cool is a waste of money unless you like just swimming in a still bay and drinking a lot of beers. Don't miss the real St. Martin/San Maarten beaches on both the French and Dutch sides.
Nassau: take a taxi @ $4pp each way to the Atlantis Resort & Casino on Paradise Island. It is a beautiful facility. A $25 tour of the dig is a great way to spend some time in this resort and at this port area.
Bon Voyage.