Some good free campgrounds in Arkansas that you can stay at for free are the campgrounds.
Allen's Ferry Little River Fulton.
Fourche Mountain Rover.
Sam's Throne Recreation Area Hagarville.
Spillway Landing Camping Area Hope.
Upper Buffalo Creek Deer Camp Waldron.
Also not camping but if you're in Arkansas and can get down to Pine Ridge Arkansas which is close to Mena Ar you should stop in and see the Lumb and Abner general store museum as it's a wonderful place to visit.
There are some other good campgrounds around Dequeen Ar, Mena Ar and many other places.