I discovered this while traveling through the West/ Southwest. Washington, Oregon, Utah, California, Arizona, New Mexico have BLM access for dispersed camping and back country access.

I was told by the staff of Big Bend National Park that Texas doesn't really have anything like that as most of the ownership rights for the land were already decided when they joined the US. They do have some great affordable places to camp in the way of National, State, and County parks. I recall paying $12 a night for full service campsites which would be up to $40 a night in Oregon/WA without the service.

The only free camping I came across was in Freeport TX on the beach but it's fairly busy on weekends. So much so ice cream trucks, sanitation trucks, and police do regular patrols as 100s line the beach in their vehicles for surf during the day and parties throughout the night. Not really a great place for quiet camping.

If you want to be a Libertarian or free country type Arizona might be one of the best places to try to do that. I just wouldn't want to try to do that in the summer in most parts of it.