U.S. 36 is a great drive. Stop in Hannibal, right on the Mississippi River, to visit Mark Twain's home and related sites -- Becky Thatcher's father's store, Mark Twain Cave (formerly Injun Joe's Cave when you could still say such a thing), the statue of Tom and Huck and the lighthouse on Cardiff Hill, and much more. Mark Twain lake has a great campground, and Twain's birthplace at Florida, MO.
On the west side of the state, on the Missouri River, is St. Joseph, home to the Pony Express and a great museum. There are several charming towns along the way, and the highway is excellent.
In Kansas, small towns like Hiawatha (ask about the special grave in the town cemetery), Washington, Belleville, and others have great attractions, and several have town parks where you can camp for next to nothing.
Have a great trip!