Is it correct grammar to say northern of a city?

No. "Of a city" needs to modify a preceding noun, and "northern" is an adjective, rather than being a noun. But "northern part of a city" or "north of a city" would both be okay, because "part" and "north" can be nouns.

I don't understand why "of a city" needs to modify a preceding noun, however (if that is really true). In some other examples, a prepositional phrase with "of" can go with a preceding adjective -- for instance in "desirous of being chosen".