dunno this is actually a confusing part of the current law, example wally world sells alcohol but not for drinking in the store, but they can sell on sundays iirc so they're a sub class D or something
my understanding is any place that sells alcohol for consumption even if it's not their primary source of income, this would include restaurants.
quite a few places are off limits, state buildings, pd's, are no brainers, every library i've been to has no weapon signs, infact quite a lot of businesses have the no gun signs up which makes them off limits..
make sure you look around the entrance real good for those signs, they're every where. you dont really notice how many there are untill you start looking for them.
btw OC is legal here if the desire arise, dunno about KY but i know some places do not allow OC.. if it happens to become visible in ohio you dont have to worry.