There were a number of suggestions in several prior threads for some if not all of these ports of call, so you might want to look through them.
The only one of those ports that I have visited as a port of call is St. Thomas. From there, I have twice taken Princess's excursion called the "Champagne Catamaran Sailaway to St. John" -- and I probably will repeat it again next time I'm aboard a ship that calls there. The 50-passenger sailing catamaran picks you up right at the cruise ship pier and sets sail for a secluded beach on St. John with a nearby reef for snorkeling. Upon arrival, the crew anchors the catamaran and lowers a bow stairway into the water for access to the beach and the water, then spreads out a cold buffet luncheon. You have plenty of time to swim, snorkel (the crew provides equipment and lessons provided free of charge), and sunbathe, either aboard the catamaran or on the beach, as you prefer, after which the crew sets sail back to the pier. Throughout the whole expedition, the crew serves complementary beverages of your choice (champagne, rum punch, beer, juices, and soda) -- and I have not heard of any instances in which any of them have run out. This expedition usually returns to the cruise ship pier around 3:00, so there's plenty of time to shop in Charlotte Amilie upon its return before the ship departs.
If you like to visit nice beaches, while in St. Maarten, grab a taxi and head out to Orient beach. There are lots of water activities there, parasailing, etc. The beach is huge, tons of lounges and places to eat and drink. Its also next store to a nudist colony, so you may see a few of them also.
In San Juan, there is the rain forest tour, which I hear is pretty good or if you just want to walk around Old San Juan, thats also interesting. You can walk up to El Morro and check out the fort, what a view! Shopping is also good there. You may spot the trolley that goes around too.
In Nassau, they have a dolphin swim that you can book on your own or take a tour. You may even want to get the water taxi over to Paradise island and check out Atlantis. BTW, when are you cruising on Century? Its always a good idea to have some set plans for the islands, have a fun cruise.
Have just returned from Eastern Carribbean on the Century (11/18).
San Juan - the ship docks too late to really do anything (4:3pm). The evening sightseeing trip is good ($17/pp). The stores close at 6:00pm despite being told otherwise by cruise staff. We were not impressed with this stop.
St. Thomas was beautiful any of the beach tours are good and if you do a beach stop in the morning you still have time to shop in the afternoon. We found the shopping to be much better in St. Thomas compared to St. Maarten.
St. Maarten - Stick to a beach tour - we did the island tour and were disappointed at the poverty and seemingly lack of development. The market place in Marigot was full of the same old stuff nothing new.
Nassau - in our opinion this stop is even more of a waste of time than San Juan - the ship docks at 1:30pm and leaves again at 7:00pm - not enough time to really do anything. The stores are chaos as there are 6 other ships in port. The shore excursions are not worth the price in Nassau - you can take a taxi and do your own thing.
First time we were in St. Thomas, we did the shopping thing. Going back in January and we are planning on taking a boat over to St. John to take in the natural beauty this time.
In Puerto Rico, we did one of the Forts and a tour of the city which was interesting. This time we are going to do the Rain Forest.
Whatever you do, you will have a wonderful time!!! Enjoy.