Missouri has several Conservation areas where camping is allowed but it is difficult to find them unless your are somewhat familiar with the state and counties. They aren't on most camping maps and sites. Kansas has a lot of city campgrounds that are either free or very inexpensive, plus you can stop overnight at their rest areas.
I always do an extensive search for enroute campgrounds when I am heading somewhere and try to choose those that I think will not be overly in demand, especially in the summer. I much prefer staying at city, county, or remote areas as opposed to Walmarts.