We spent two nights at Babler State Park which is west of downtown St. Louis. It has a very nice campground located on a forested ridge in a large state park. There are electric hookups but you have to tote water from the hydrants. Bathrooms well maintained. Sites are paved with concrete and very level. There is not a lot of vegetation between most of the electric sites but they are spaced well apart.
It's not centrally located but the major tourist sites are a short drive away. It was brutally hot when we were there (100+) but that seemed abnormal.
I'll stay there again if I visit the area or pass through.
http://www.mostateparks.com/babler.htm