We ended up staying at Cottonwoods RV Park. It was nice for a commercial RV "park" and had excellent facilities including one of the nicest shower houses we've ever seen. It was still just a commercial parking lot and did not give the "back to nature" experience that we usually look for and find in state parks, but it did very nicely as a safe, convenient place to stay while visiting our son.
On this trip we also stayed at Fort Massac State Park in Illinois, Oak Mountain State Park in Alabama, and Trace State Park in Mississippi. I must say that I was quite shocked by the poor facilities at Fort Massac. The Alabama and Mississippi parks put it to shame, (and Mississippi is the poorest state in the union). If I get around to it I'll put in reviews for these parks.