We didn't schedule an excursion through the ship but scheduled an all day snorkeling/beach tour with Capt. Bob /Soualiga Destinations. The seas were a little rough that day so we didn't get to snorkel or see much sea life because of the low visibility but it was a blast anyway. You go out with a small group of people, they provide all the drinks and a great lunch and it's a lot of fun touring the island and beaches in a speed boat!
We did our own thing in St. Thomas. We took a cab over to Magens Bay and rode the tram up to Paradise Point. It was rainy at Magens Bay so we didn't get to enjoy the beach much but I'm sure it's very beautiful in nicer weather. The bar up at Paradise Point is a great place to sit and have a drink while enjoying the view. We visited the shopping center at the port and got a few bottles of water and soda which were reasonably priced. It was also a good day for us to catch up on e-mail and check in with family back home. Our carrier is AT&T and there were no extra charges to use our phones that day since we were in the USVI.
Nassau was cloudy and cool the day we visited so we decided just to stay near the port. We walked down to the restaurants past Junkanoo beach and had some lunch and then stopped and had a drink at Senor Frogs before heading back to the ship. The little straw market that you walk through at the port has free wi-fi, it was very slow though we were able to use it to check in for our flight home the next day.