They're called Booking Zones. If you have two theatres in the same Booking Zone then they split product. Sometimes something goes one place, sometimes the other. Also in a competitive Booking Zone, theatres might bid on a film.
If you have your Booking Zone to yourself, then you may play whatever film the distributor agrees to give you. But note the sentence structure. You agree to play the film the distributor agrees to let you play. You don't demand to play something and they shouldn't insist you play something. Although they do pressure you to play things sometimes.
It's a relationship like any other. There is give and take. There is compromise and there is sometimes strife, But if you are good and they are good, you both get to make money off of the deal and then you both are very happy.
A Booking Zone is usually inside a 3-5 mile circle. But it can also be dozens of miles or more. It depends on the type of theatre, population and competition. And no, the theatre doesn't get to dictate the Booking Zone.