There's quite a bit of public hunting areas in Ohio. Ones around me are Killdeer Plains, just south of Upper Sandusky, and Delaware State Park, just north of Delaware. Killdeer Plains is not bow only, but has lots of deer, but takes some scouting to find them.( http://www.dnr.state.oh.us/wildlife/pdf/pub23.pdf)I grew up just west of Killdeer and hunted it most of my younger years with my dad and grandfather.
Delaware State park allows bow only within the park limits and you can camp right there at the campgrounds and hunt. (http://www.dnr.state.oh.us/parks/parks/delaware.htm) Also has Public hunting area around it. I bow hunt Delaware every year for a week and see deer everyday.