I'll tell you the michigan way of finding Bay City. Get out your lower Michigan map (yes you have one, it's your right hand). Look at your right hand with the palm facing you. Take your left pointer and push down in the gap between your fingers and thumb, push toward your wrist. The place where your finger stops is in Bay City, that gap between your fingers and thumb is the Saginaw bay.
Arent you referring to the " Bay State" ? Massachusetts bay dominates the state's coast! yes, Massachusetts is the Bay State.
I havent heard of the BAY CITY!