I did the Sensation in September and it visited Freeport and Nassau. In Freeport, I did some tourist shopping and stopped and had a couple of drinks at a bar near the port. I had no problem. I did not take any tours.
In Nassau, as soon as you get off you are at the terminal. You can pick up some local "hot sauce." Their prices on t-shirts and stuff is just as good as at the straw market. In fact the quality is better at the terminal.
The straw market, down the street, you can get a silver tone bracelet for about $10. There is a Senor Frog's, near the straw market, that is a tourist place, where you can stop for a bite to eat and drinks. They usually have the music going. Depending on the time you go there, it can become a party place.
The Pirate Musuem is within walking distance. You can also get a "Starbucks" coffee close by.
You could also take a horse and buggie tour of the city.
Go and enjoy yourself. Inquire at the tour desk about what is available for tours and what within walking distance of the ship.