There's ton's of public hunting areas in and around Hocking Hills. It's right in the middle of Hocking state forest. One of the better areas in the state for Deer. Not nearly the pressure as some of the more highly touted counties. I'd look for places on the northern end or around Tar Hollow state park. A little flatter and closer to agricultural areas. Here's the link to the ODNR site. http://www.dnr.state.oh.us/forestry/Forests/stateforests/hocking.htm

Keep your eye out for private lands. They are dispersed through the state forest. Usually posted and marked with yellow paint boundries. But not always.

Stay away from Burr Oak. They do not have public hunting.

Another good area is Zaleski State forest. It's one county south of Hocking. It's a huge area of public hunting. Not as much pressure here, but the terrain is much rougher and there aren't as many roads to get around. Not much in the way of agriculture here, but plenty of mast for the deer to feed on. The deer also tend to be a little smaller here. Some of the hills in this area have slopes ranging in the 11-13% grade. If adeer happens to drop over the hill, it can be a rough time getting him to the top and out. Same senario with the private lands, not quite as many though.
http://www.dnr.state.oh.us/forestry/Forests/stateforests/zaleski.htm

Hope this helps.