IMHO: The best place for information on OC in Ohio is the Ohio sub-forum at
www.opencarry.org (AKA OCDO)
What has been stated already is correct, unlicensed OC (and licensed OC) is legal, and has OH Supreme Court backing. I do not believe with the Court ruling a local government entity can do much to restrict your OC any more than the general restrictions on any carry (like courts, schools etc)