They are both correct, but mean different things. "Of" is definitely the more common choice, however.
"Symbol of our city" means "our city's symbol" and describes possession. In Japanese, you would say "わが町のシンボル”
"Symbol for our city" means that the symbol somehow exists for the (benefit of the) city. This would sound like "わが町のためのシンボル”
I hope this was helpful!