We were only there on Legend from 7am-2pm. They don't clear passengers to leave until 8am and you must be back aboard by 1:30pm.
The taxi to the waterfront in town at Fort du France is $8 per cab. Ask for the ferry to Pointe du Bout. The ferry is $6 per person round trip, and takes about 20 minutes. Ferries leave about every 30 minutes. At the landing at Pointe du Bout it is a bit like a village in southern France. Shops, restaurants, the marina. Two of the hotels, close to the ferry landing, the Meridian and the one directly across from the landing, offer free use of their beach. We went to the Meridian. They have cabanas, chairs for rent for $5 each, a bar, etc. The sand is white sand, probably imported to the hotel beachs, since much of the sand on Martinique is black volcanic sand. The swimming is nice in areas sheltered by breakwaters. The snorkling along the breakwaters, and at the point of land near the helicopter landing area is great for snorlking with lots of fish. After a few hours on the beach, take the ferry back to town. It drops you at the south end of the city park, and there is sort of a flea market there. It is only 1 block from the beginning of the central business/shopping area. See the church, the library, the central market filled with fresh spices and fruit, and shop in the many boutiques. Many bakeries. Just a block and a half west of the landing is a bar/restaurant called The Crew with french wine for $1.50 a glass, and was packed with locals at noon. The taxi back is $8. You could have the taxi take you back to the Sea Explorer Duty Free shops in the port for liquor, free rum samples, and various other duty free items. They will shuttle you back to the ship, too.
They warn that trying to do much more on your own in the limited time available is pushing it. Maps that make distances seem short are deceiving, as distances are much longer than they appear due to mountainous winding roads. It really takes more time than you will have available. To see the more distant places like St. Pierre, where the volcano erupted wiping out a town 90 years ago on the North tip of the island, you would need to take a ship sponsored tour, to ensure they get you back in time, but those who took it said they spent almost the whole tour on the bus, except a self-guided tour of the rum factory.
Martinique is one of our favorite places but the visit is always short. I think the port discourages the ship visits lasting late in the day. I'd like to spend several days there sometime.
