Ohiofag here, from the SW area.
Over by Yellowsprings there's a giant area of parks connected, Glen Helen Preserve, John Bryan State Park, and Clifton Gorge. Incredible trails and a fairly large area all together. If you park at Glen Helen it has good access to the towns but a $5 fee. Don't park at any of the Clifton entrances or your car will be broken into.
Germantown Metropark and Twin Creek Metropark over by Kettering is really pleasant with some terrain that doesn't even really feel like Ohio in some spots. There's a connector trail between the two of them that connects them all together called the Twin Valley Trail that's a total of 22 miles. It's got a lot of steepness for Ohio, a lot of it situated on an Indian fort.
Caeser Creek Statepark is nice for fucking off in a random direction. There's a big loop at the bottom around the lake that's flanked by some pretty big unmarked sections that are reserved for hunters, but you can just slip in and disappear in the off-season.
Wayne NF is a blast. National Forests have much more relaxed rules than parks, so if you're into bushcrafty shit, it's a good time. Just make sure to take your shit down when you're done.
Zaleski SF is similarly lax. Really good destination for backpacking, cheap and good backcountry sites and a lot of trails. Also has a couple of historical sites if you're into that, there's an old iron forge and a few pieces of related abandoned infrastructure in the area.
If you're looking for a drive, Red River Gorge remains the top of my recommendations. It's in Kentucky, so a bit out of your way, but it's a must for any hiker in range. Massive sandstone cliffs and seriously challenging trails.
Another anon mentioned Hocking Hills, I'll second that. It's a great place to hike more technically challenging trails if that's your thing. Lots of unique and technical rocky trails.
I've not been to some Shawnee SF but have heard good things about it, same for George Washington NF.
