In St. Louis, we enjoyed the St Louis West KOA in Eureka. Even though it is outside of the city, it's easy to hop on the interstate and get to the main attractions. I wrote a longer review and have some photos of it here:
St Louis West KOA.
We haven't camped in KC since we've had a trailer of our own, but several years ago, we stayed at a really pretty state park outside of town called Watkins Mill. It has historic sites and a trail to explore. We also stayed at the campground at Worlds of Fun, and I remember thinking it was nice (but again that was many years ago).