Airspace is regulated federally in most countries, but what you can build on the ground is almost always local in regulation.

You might be allowed to fly overhead without he city being able to do much about it, but you won't be able to land or take off.

(And to be honest, if the city complains to the federal regulators regarding noise, they almost always listen - almost every airport in a town has strict noise-reducing approach patterns for this reason already.)