where is bay city?

There's no Bay City in the SF Bay Area. There's "the Bay" and there's "the City" but not the combination of the two.

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!

Bay city is in Michigan, it is about 150 miles north of Detroit, and about 20 miles north of Saginaw MIchigan.

Since you're in the San Francisco section, there is no Bay City. SF and its environs are called the Bay Area.

in Michigan?