Open Carry is legal in Ohio but it makes a big difference if you have a concealed carry license recognized by Ohio. If you don't have such a license, you cannot:
1. Carry a loaded handgun in a motor vehicle. (See below to see how restrictive that is).
2. Carry in any bar/restaurant/grocery store which has a class D liquor license and is serving for on premises consumption.
Also, there is no legal definition of "open" or "concealed", so make sure your gun is very openly carried so the wrong cop doesn't decide to arrest you for carrying "concealed". In one case in Cleveland, a guy carrying openly in a military style flap holster which generated three calls to 911 for MWAG, still got arrested for CCW.
It's very important to understand Ohio's legal definition of "unloaded" which has no relationship to commonsense.
Some links on Ohio law:(5) “Unloaded” means any of the following:
(a) No ammunition is in the firearm in question, and no ammunition is loaded into a magazine or speed loader that may be used with the firearm in question and that is located anywhere within the vehicle in question, without regard to where ammunition otherwise is located within the vehicle in question. For the purposes of division (K)(5)(a) of this section, ammunition held in stripper-clips or in en-bloc clips is not considered ammunition that is loaded into a magazine or speed loader.