Best thing to do first is go to this link
http://www.dnr.state.oh.us/wildlife/tabid/6522/Default.aspx You can get all the info on regulations, tags, bag limits, etc. Also there are links from that page to maps of public land wildlife areas.
I hunt private land in the middle of the state, so I cant be much help when it comes to public land. The south eastern part of the state is usually regarded as the best bet. The is quite a bit of public land down there. Zaleski SF is well regarded and I have heard good things about Shawnee SF (more south central I believe).
Sorry I cant be more help, but the ODNR site is a good place to start.
BP