I usually do the camp thing when I go on float trips. So I have great suggestion if you want to go canoeing as well (I'm sure you can just camp as well. but this isn't a secluded type campsite):
It's about 3 and half hours south of KC off I-49 (71 highway) in Noel, Missouri.
Shaded campsites, clean shower and bathroom facilities, they have a quiet area so you don't get stuck with all the party animals, unless you want to. They have little shop where you can get firewood, and down the road in Pineville is a Walmart so you can pick up whatever you might have forgotten to bring. (We usually make at least one trip there.) It's right on the river so you can swim or fish. Close to Bluff Dweller's Caverns and Spanish Treasure Cave.
I've only been there on weekend and even though it can be busy, I never feel like the river is over-crowed, and for the most part, people are very friendly. I bet if you went during the week, it would be less busy.
It's also very pretty country. The landscape is gorgeous since it's the foothills of the Ozarks.