Either Oyster Pond, French Side, past captain' s Oliver, there is a path that takes you down to the very entry tip at sea of Oyster Pond Lagoon, or at Mullet Bay where the old old casino used to be, past hole 17. All depending on sea conditions
Never tried but I would not be surprised that the spot is a good one given the presence of caves and rock formations that could foster the presence of several species of fish. Oyster pond there could be a chance of catching some tarpoons or snooks(sergeant fish) which can deliver a good fight to bring them ashore, although tarpoon is more worth to release them. This of course fishing the waters on the inside part of the lagoon.