OK, this is my 'where to ride in Ohio' rant:
I live in Springfield so I only know from I-70 south.
For stuff up north some one else will need to speak up.
So, starting on I-70 there are 2 pay to play places at the extremes of the state.
Haspen acres is in Laurel Indiana, just across the border.
Haspen is pretty much scorched earth, 640 acres that has been ridden on for years.
But I keep going there for one reason or another, they have some special events there from time to time.
Haspin Acres - home
At the east end of the state is Power Line Park.
Never been there, they host a GNCC woods race there late in the season.
Home Page
The state forest has 4 APV ride areas (Pike, Perry, Maumee and Richland Furnace).
The state has a 62" rule, but a P1000 should be able to skate on that.
Also, state APV registration is required but it's free to ride.
Pike is small but very scenic, great for a shake down cruse.
https://forestry.ohiodnr.gov/portals/forestry/pdfs/SF/pike_apv.pdf
Perry is reclaimed strip mine.
Its advantage is that you don't need to stay on the trail.
https://forestry.ohiodnr.gov/portals/forestry/pdfs/SF/perry_apv.pdf
I haven't been to the other two.
http://forestry.ohiodnr.gov/Portals/forestry/PDFs/SF/richlandfurnace.pdf
https://forestry.ohiodnr.gov/Portals/forestry/PDFs/SF/maumee.pdf
Wayne national forest also has trails but they are width restricted to 50".
I've never been but heard good things.
They require state APV registration and NF fee to ride.
The trails can get crowded on holidays and they are heavily patrolled.
Wayne National Forest - ATV
The other areas to consider are the Hatfield McCoy trails in West Virginia and the 3 systems in Tennessee (Royal Blue, Brimstone and Windrock).
All of these places offer very scenic riding and camping / cabins that are ride to the trails.