I am not far from you in Parkersburg, WV. We camp more in Ohio than any other state.
Not a State Park, but we like Wayne National Forest in Ironton. There are 2 campgrounds there and the COE lake. We camp at Oak Hill
http://www.fs.usda.gov/recarea/wayne/recreation/camping-cabins/recarea/?recid=6206&actid=29We also like Salt Fork off I77 in SE Ohio.
http://parks.ohiodnr.gov/saltforkIf you bike or kick scoot,try Coshocton Lake Park. I love that it is surrounded by the Three Rivers Bikeway.
http://www.coshoctonlakepark.com/You might try Happy Hills campground in Nelsonville instead of Hocking Hills. It is a private campground, not state park, though. Still close and easier access. You can get a bison burger at Rocky's Outfitters in Nelsonville There is also the Hocking Hills Flea market complex near Logan.That campground is probably the easiest for you to get to - Rt 7 to 33.
http://www.hockinghills.com/happyhills/