Places in Missouri where we have enjoyed camping in our r-pod. We mainly like to hike, bike, and swim...don't boat or fish much.
Smithville Lake - just north of KC - not many trees but great bike path and lake.
Weston Bend State Park - also just north of KC - no swimming but lots of trees and great hiking trails, plus bike path to historic town of Weston.
Watkins Mill State Park - just north of KC - probably our family's favorite campground...lots of trees, lake for boating/fishing with nice, sandy swimming beach, and awesome wooded bike path. Nice large, private showers.
Bucksaw on Truman Lake (corps park) - just SE of KC - biking is OK, plus nice sandy swimming beach and lake for boating / fishing.
Pomme de Terre Lake - SE of KC - two campgrounds (Pittsburg and Hermitage) ... more trees at Pittsburg side of lake. Rocky lake but cleaner water than Truman, a muddy/dirty lake.
Table Rock - near Branson - nice lake, plus short but good bike path. (Can't remember about the trees -- only went there once!)
Wilderness at Silver Dollar City, near Branson - mostly used for pit-stops when we are hanging out at the theme park. :D Shuttle bus from park to SDC so you don't have to take your car. Small but clean bathrooms.