The Barter Theater in Abingdon, VA is right across the street from the Martha Washington Inn (formerly Marsha Washington College back in the day). Also, if you are interested in Thomas Jefferson/architecture, his “mountain” home at Poplar Forest, in or outside of Lynchburg, VA, might be worth a stop; Monticello plus Poplar Forest could be interesting.
In Tennessee, the Big South Fork National Recreation Area on the Cumberland Plateau has some nice hiking trails (elevation changes are very reasonable), and there is Rugby, TN, a community started in the 19th century for the younger sons of English nobility: Rugby, Tennessee - Wikipedia