Richard Connell's "The Most Dangerous Game" begins with the protagonist, Sanger Rainsford, on a yacht. The ship's captain, Whitney, is sailing his vessel in the dark past a mysterious and rather foreboding island which the sailors all refer to as Ship-Trap Island.
The first hint we have about the ship's location is that the narrator tells us Rainsford looks out into "the dank tropical night," so we know we are in a tropical climate. When Whitneywatches Rainsford try to see the island, he tells the renowned hunter that
"even you can't see four miles or so through a moonless Caribbean night."
We know, then, that the yacht is sailing through the Caribbean Sea.
Our last bit of evidence is their destination: the ship carrying Rainsford is on its way to Rio de Janeiro so Rainsford can hunt jaguar "up the Amazon" River.
It is evident, then, that Ship-Trap Island is in the Caribbean Sea.