Just in case you didn't know it, there was a real Tortuga in the Caribbean.
In 1503, on his last trip to the "New World", Christopher Columbus discovered a small group of 3 islands. They were totally wild, and literally covered in turtles. He claimed these islands for Spain, and called them Los Tortugas.
Today they are part of the British West Indies, (BWI), and are the islands of the Caymans. Grand Cayman, Little Cayman, and Cayman Brac.
They sit straight south of Cuba, about an hour and a half flight from Miami.