What are the places that Rainsford goes on the island in The Most Dangerous Game?after the chateau
After leaving the chateau, Rainsford knows that he has to win this "hunt" in order to survive. He got a 3 hour head start, and doubles back a few times and then rests in a tree. He waits there until Zaroff comes right near him, but realizes that Zaroff is playing with him. So he waits until Zaroff is gone and then moves on to another area.
He sets a trap for Zaroff in the forest where a dead tree would fall on him. Unfortunately, only his shoulder is hit, so when Zaroff goes back to the chateau to clean his wound, Rainsford moves on to Death Swamp where he sets up another trap that ends up killing Ivan. After that, he jumps off a cliff into the sea in order to escape. Meanwhile, Zaroff heads back to the chateau again, and we don't know where Rainsford is or if he's ok. He does make it though, because when Zaroff opens the door to his bedroom, Rainsford is waiting for him and ends up feeding him to his own dogs.
So the different settings on the island are the jungle, the Death Swamp, the sea, and it ends up back at the chateau.