Is it correct to say "You've been living here for too long"?
Or is it better to drop the for? "You've been living here too long."
Is either preferrable over the other for some reason?
Either one is fine. However, the sentence with for is better than the one without, because the former is more explicit than the latter.
At the end of the day, it is up to one's convenience to drop it or make it explicit.