A good bit of the trail is in the state park, so I assume they want you to camp just at the shelter sites. The shelter sites are pretty good, so I'll stay there if we go again. I only saw 1 day hiker when we were there and a couple horses – so don't worry about crowds. It is much better than deam- and you don't have the crowds or horse trails to deal with.
My son enjoys hiking – and does not require a lot of scenery to keep his interest. We both like to get out and explore – and just try to check out most of the longer trails in the area.
The other local trip we did last year that was interesting was the Tecumseh trail. The trail is a bit overgrown in places and has some road walks. Its pretty reasonable terrain for kids – we did 35 miles over 2.5 days The highlight of that was camping at yellowwood lake – at the campground. When other campers found that my son had hiked in, they were amazed and loaded him up with candy and other junk food. He loved it.
Still, his favorite is the red river gorge. You can get there in 4 hours from Indy (vs over 3 hours to get to the AHT).
Another option to consider is brookville lake- Adena trace trail. It is a 24 mile loop around the south half of the lake. I did a day hike there a few weeks back to scope it out and we will try to do the loop in the spring before the boaters fill the lake. The only place they allow camping is at the campground, but it is right off the trail – so I think it would work. It really is a pretty area.
A couple other things have popped up on my list too. I found some info on the twin valley trail just outside Dayton, Ohio. The trail links two metro parks in the area, and passes close to downtown Germantown. It is around 2 hours away so we will probably try it out this year.
I also hear that the backcountry at mammoth cave is nice. I've hiked the front country trails there, and am interested in venturing into the backcountry there. They are multi use (ie horse) trails, but at only 3+ hours from Indy it is reasonably close.