Where did the kidnappers take the boy in "The Ransom of Red Chief"?

In “The Ransom of Red Chief,” the two kidnappers take the little boy to a cave on a mountain. We are not told much more about the place where they take him.

According to the narrator, this story takes place in Alabama, near to a small town called Summit. The two men, one of whom is narrator (we find out later his name is Sam) and the other of whom is named Bill, pick out the target of their kidnap plot. They then prepare the place where they will take the kidnapped boy. Here is what the narrator tells us about the place:

About two miles from Summit was a little mountain, covered with a dense cedar brake. On the rear elevation of this mountain was a cave. There we stored provisions.

After they store the provisions, they go into town to kidnap the boy. He puts up quite a fight, but they eventually get him into their buggy. At that point, the narrator says,

We took him up to the cave, and I hitched the horse in the cedar brake.

From this, we can see that the two kidnappers take “Red Chief” up to a cave on a small wooded mountain about two miles from the town where the boy lives.

Where do the kidnappers hide the boy in "The Ransom of Red Chief"?

After Sam and Bill kidnap the boy, they hide him in a cave.

The story involves a kidnapping that turns into a captivity of the kidnappers by the kidnapped child who views his kidnappers as his new playmates subjecting them to all types of attacks as he plays rough.  The boy manages to inflict great pain on his kidnappers through the course of his playing with them.

As Red Chief, Johnny manages to turn the criminals into the victims in this comical short story.  In the end, the kidnappers have to pay Johnny's father to take him off their hands. 

"The father demands a ransom of $250 from the kidnappers, in return for which he will take Johnny back. Bill, who has already tried to send Johnny home, begs his confederate to agree, and Sam himself is now willing to pay to get rid of the child whom the con men had abducted."

"Johnny, however, does not wish to leave his captors. They must scheme to get him back to his father as once they had schemed to get him away from home, and finally, they must run at top speed to escape the boy who does not wish to lose his new playmates, the would-be kidnappers who have become his victims."