Biltmore estates in Ashville, NC. It was built by the Vanderbilts and I think is one of the few remaining true estates left in the US. Here is the link Easily spend a morning if not more there. BTW its’ also an Olmsted design.
Clingmans Dome isn’t far from there. Has great views (on a clear day) of the smokey mnts. Four states are visible.
If your coming across through southern IL, Garden of the Gods is another possible spot to take an hour or two break.