This is a much better place to get info about Ohio's law than just from me trying to repeat it: http://www.ohioattorneygeneral.gov/ConcealedCarry Check out the link on the right hand side for the Concealed Carry Manual.
You are not allowed to carry in any place that serves alcohol for consumption on site. There is a duty to inform LEO's. Car carry is somewhat normal now, it can be concealed on your person. I have never heard anything prohibiting BUGs. And signs are covered by law.