There is only one RV park in the area and it is in Shawnee called Walnut Grove RV park. Here's the web site. It is small, but my brother inlaw has stayed there in his 40+ft rig.
There are a few others near by. One in Bonner Springs/Kansas City, KS (15+ mi from Overland Park) called Cottonwood Camping. I've never stayed there but it is packed when nascar are at the Kansas Speedway and it's right by the Legends shopping center.
Then another in Lawrence, KS (30+ mi from Overland Park) it's a KOA.
There is also a KOA out east of Kansas City, Mo in Oak Grove but it's about an hour from Overland Park.
Hope this helps.