You're right. I usually hear "off" is collocated with"coast".I don't know why I forgot that!I must have been stricken in years.Yes, certainly, though I'd use a different example: A bomb went off off the coast of Brazil. 'Off our city' doesn't quite sound right.
Good point, Fab. My wife is often confused when things can either go "off" or "on", or both. (Bombs, alarms, lights, bells). I am always at a loss to explain it to her.The double "off" can be avoided easily by saying/writing, "... a bomb exploded off ..." Ditto with "detonated."