Berkley West Virgina comes to mind. Been out there a few times white water rafting
and riding bicycles. Pretty awsome trails along the Rivers. Most of the trails that we were on were old railroad trails owned by the Dept. of Natural Resources meaning they are maintained. If you were to go that direction, check out the White Water Rafting as well.
Knobstone is probably the best trails for what you are wanting to do, at least that I can think of at the moment.
I hiked the hell out of Knobstone when I was training for a Rockies expedition, and if I recall correctly some of the Knobstone trails are actually pretty challenging, but I haven't been out there in a bunch of years, however I think I am going to make it a priority to take my daughter out there and do some hiking this spring.
If you're looking for a loop trail check out Harrison-Crawford Forestry. Thay have at least one overnight trail that is 42 miles (AHT-Adventure Hiking Trail) with half-face shelters along the trail to sleep in. I haven't hiked an overnight there but we camp in the electric campground a lot. They also have several short hiking trails. It's about 7 miles west of Corydon along the Ohio River.
Here is a link to Obannon State Park. The state park is surrounded by the Harrison-Crawford Forestry. DNR: O'Bannon Woods