I really wouldn't want to camp off the FS roads though unless you can find a spot waaaaay off the road. In AR, "backroading" is pretty popular. Basically, in the middle of the night, hs/ college students drink and drive down the FS roads and take turns shooting street signs/ trees/ raccoons out of the truck window. I visited a friend at Arkansas Tech and that's literally all they did on the weekends.
So much this. Similar story, different location, same state: The wife and I tried overnight camping in Hobbs before our son was born. Hobbs is a state park, mind you. And yet we woke up to drunk kids shooting at the shoreline from flat bottom skiffs on Beaver Lake at 3am. We were about 100m from the shoreline in a clearing, but having been downrange of ordinance before, it was enough of a "trigger" to make us break camp and hike back to the car at 3:30am.
It's a bit... artificial, but Lake Fort Smith has some decent improved campsites.
If you're willing to head an hour or two off of I-40 there's Mt. Magazine or Hot Springs (Hot Springs has a great ORV/OHV park). Again though, not much in the way of proper offroad camping (like you find in the desert southwest), but the improved campsites aren't terrible as a last resort.
Ref: Mt Magazine area, the wife and I camped once at the Horse Camp off of Sorghum Hollow Rd in Subiaco and it's basically a dirt parking lot with some set-back tables and hitching posts in the treeline. That area is basically all dirt forest service roads, I took them in my lowered Volvo with low profile tires and really soft aluminum wheels without issue. There are mountain bike, ATV and hiking trails in the area. No flush toilets or potable water.
Keep in mind most of what I mentioned are on state park / national forest land and require a permit for overnight camping. If you're into a guaranteed, improved spot, arkansasstateparks.com has a limited reservation type system you can use for some of the more popular places.
Arkansas, for all the crap I talk about it, isn't that bad. Just bring bug spray.
Good luck and enjoy your trip!
