I have an uncle (by marriage) who lives in SAN and is a pilot based in STL. He flies in, either jump seat or revenue, when he needs to get to work and flies home when he's done. I was on a DL redeye from SEA to JFK with what seemed like a full crew (3-4 folks) heading over to JFK to start a trip. They were all deadheading but in F actually.

Crews can live anywhere and be based somewhere else. They just have to be very careful about making sure they get to work on time. There are also crews that are on reserve that do have to be very close to the airports. They are generally junior folks and live (or stay) nearby. That's where you'll find the extra crew to cover when someone gets ill or there are other delays that prevent the assigned crew from operating a flight.