Sundermeier is the campground in St. Charles. It's close to Old St. Charles. Personally, I stay at Casino Queen. Lots more to do downtown. Great view of the arch and you can take the Metro into city or across the river one stop to Laclede's landing for food/drink.
An afternoon in St. Charles is more than enough time.
Branson has lots of great campgrounds and most all are good. We usually stay at Musicland Kampground because it's right off the strip and you can walk to several things. State Park is away from town all the hustle/bustle.
