How close can FM radio transmitters be?

Geographically close to each other ?

They can be in the same room of the same building, with their antennas on the same roof or tower.

Close to each other in carrier frequency ?

Your radio probably can't separate them if they're less than maybe 400 KHz apart.

Physically close to you ?

There's no danger to you if you're standing in the room where the transmitter is installed,

but you probably don't want to stand in front of the antenna for too long.

Driving past the station's transmitting antenna is no problem for your car radio.