The three main locations in the book are the firehouse, Montag's home, and the woods near the river where he meets the other rebels. Each one represents a portion of Montag's life, and each one corresponds to the three parts of the book.
The firehouse is the place that the government controls and places their controls on the people. They spy on the populace with the Mechanical Dog, and they encourage the citizens to report their neighbors for any infraction of the rules. When they finally show up at Montag's house, Montag asks if his wife turned him in. Beatty nods,
"But her friends turned in an alarm earlier that I let ride. One way or the other, you'd have got it." (pg 117)
The second location, the home, is a place of transition for Montag. It is where he does his thinking. When he first meets Clarisse, he has a discussion with her, but he really thinks about what she says when he goes home. He wants desperately to talk these ideas out,but Mildred only wants to tow the government line and listens to the "family". He gets sick at home after he sees the woman die with her books. He tells Mildred,
"There must be something in books, things we can't imagine to make a woman stay in a burning house; there must be something there. You don't stay for nothing." (pg 51)
When he calls in sick, Beatty comes to the home and tells him that the governments philosophy was to,
"Whirl man's mind around about so fast under the pumping hands of publishers, exploiters, broadcasters that the centrifuge flings off all unnecessary time-wasting thought!" (pg 55)
It is here, at the home, that Montag needs to make a stand. He can go along with his arrest, or he can flee and start a new life. After he kills Beatty, he is on the run. He thinks of giving himself up. But then he thinks,
"No, we'll save what we can, we'll do what there is left to do. If we have to burn, let's take a few more with us."(pg 122)
He escapes the Mechanical Hound and the massive news media blitz asking people to report any sightings of him, and he floats down a river to the place out in the woods where he meets Granger and the other men. He sees them as his future and his freedom. This is the third location. After the atomic bomb hits, he finds himself with these men and thinks,
"I'll hold onto the world tight someday. I've got one finger on it now; that's a beginning. (pg 164)
He has figured out that he can begin a new life here.