A few years ago, I spent a week at the Shady Lake National Recreation Area. It's one of the few National Forest campgrounds I've stayed in that has flush toilets and showers. I was there for the hiking, not the riding, and have been meaning to get back there ever since. Lots of twisty pavement and lots of dirt/gravel forest roads. To find it on the map, locate Athens AR, and Shady Lake is about 4 miles NW on Route 246.
Another nice place, right on the Talimena Highway, is the Winding Stair NF campground. The problem is that their well ran dry a few years ago, so there's no water in the campground - you've got to bring water with you. On the plus side, you'll probably have the entire campground to yourself, including a majestic view, since the campground sits right on top of the ridge.
EDIT: If you want amenities, there's also Talimena State Park. It's right at the western end of the Talimena Highway, about 3 or 4 miles outside of the little town of Talihina OK. Prices are reasonable and, depending on if you're tenting or RVing, you can choose between some quiet, private little tent sites for only $10/night, or RV sites for (I think) $20/night. The RV sites have electricity & water. In either case, you get flushers and showers.
Whether you choose Okie state parks or NF campgrounds, campers 62 or older get a 50% discount.