Check out the National Forrest areas of both states, We were just at Blanchard Springs Caverns (the only show caves managed by the Forrest Service, and quite wonderful to tour) and there are several unimproved campgrounds that have no charge to use, we stayed at the campground at Blanchard Springs, for $5 per night, ($5 with the Age or Access pass, $10 without) and wonderful swimming holes. No hook-ups though. We were the only campers there, beautiful and quiet.
The Forest Service Headquarters and offices have folks that are also very helpful, check with the rangers at the parks.
Get a copy of the DeLorme Atlas and Gazetteer for MO and AR(available at most/many sporting goods stores) and get out and poke around.
I figure most folks don't want to share their special places on the 'net for thousands of others to know about. Hard to keep them secret then, eh?
There are lots of places in the Mark Twain NF where you can dry camp. Also you can check the MO. Dept. of Conservation website and find Conservation areas in SW MO. Some of these will have camping that is free.
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One wonderful life partner, my wife of 40 years
"I want people to know "why" I look this way.
I've traveled a long way and some of the
roads weren't paved."