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!

Basically they mean the same thing. However, depending on context they could slightly infer slightly different meanings.

Thank you, everyone! It's so subtle but now I see the difference.

of: if you mean that it is a part of the city and it becomes a monument or a celebrity for:it wasn't a symbol and willingly it decided to become a symbol to answer the need or the good of your city so in your case i guess you mean of maybe am wrong,

It has become the symbol "of" our city :)