Where did the kidnappers take the boy in "The Ransom of Red Chief" by O. Henry?

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.