BarbyandLeo,
Not sure if you still can do it but you used to be able to go to the Marigot Market early on market days and purchase fresh fish from the fisherman there close to the waters edge. About as fresh as you could get I would think. But you need to get there early because you might find yourself competing with some of the local restaurant Evers for the pick of the catch. Wednesdays and Saturdays used to be the days they brought their catchbin.