Another option would be the Ozarks or Ouachitas in Arkansas. Since they're a little higher in elevation, it's a little cooler there by 4 or 5 degrees. Plus, they're on the way from Detroit. Lake Ouachita is amazingly clear with a variety of camping options including COE and an SP. Besides the usual outdoor activities, there are interesting museums in Hot Springs and Little Rock and a great free art museum in Bentonville (Crystal Bridges). Plenty of little streams to play in.
I was in Hot Springs AR last August and it was hotter than 10 kinds of hell. Humidity is a b**** and with all the tall trees, it never seemed like we could get a decent breeze blowing thru the campsite. I think that part of Arkansas would be beautiful in late fall of early spring.