Try some of the state parks. Weston Bend is located in Weston MO, just a few minutes north of KC by I29. Weston also has 3 nice wineries if you are interested. Shaded but not wooded, but they do have nice walking trails that leads to an overlook of the Missouri River. To the northeast of KC about 20 min is Watkins Mill State park close to Kearney and Excelsior Spring close to I35 highway. If you want to stay in KC there is the Jackson County campgrounds, Longview, Lake Jacomo, and Blue Springs Lake. All county ran. Smithville lake has 3 campgrounds, they are COE but ran by Clay county. There is also Basswood in Platte City. Watkins Mill (one of my favorite) is pretty wooded but sites are electric only with water and dumpstation when you enter the park. Jackson county campgrounds have shade but not as private. Full hookups are in full sun.
2005 Chevy 2500HD
2013 Flagstaff 8528BHWS