We also stopped in Nassau, but I don't see that in the choices. Charleston was the embarkment port. And while it was awfully crowded, they are really organized and disembarkment when we came back was as smooth as butter. Didn't see much of Charleston because we were near the seaport and train station and those are usually not the prettiest part of the town. My understanding is Charleston is a nice city.
As far as Nassau - immediately next to the ships (its a little bit of a walk) you enter a building that has shops selling food, jewelry, etc. You then enter an area where you can rent a horse buggy ride or take a boat ride to other parts of the island. There are duty-free shops and other shops along the boulevard. You can walk a little distance to a tiny beach where the young owner has a shack that sells food and drinks and he rents you a beach chair. He was nice and let us sit at a table and use a couple of chairs without charge since we bought a couple of virgin drinks. The water was kinda cold (compared to the beach at Tybee in Savannah) and very salty. Again, we were lazy and didn't take a water taxi. The prices were cheap about $6 per person to take you over to Paradise Island.
If you make the effort and take a cab, you can get over to a hotel resort and enjoy the beach and other activities.