Greeneville is a small East Tennessee town with a surprisingly dense slice of early American history. It was the home of Andrew Johnson, the tailor who became the 17th president after Lincoln's assassination, and the National Park Service preserves his shop, homes, and grave in the middle of town.
The town also has the odd frontier story of the State of Franklin, a breakaway would-be state that briefly tried to exist between North Carolina and the future Tennessee. Add the Dickson-Williams Mansion, the Greeneville Greene County History Museum, and a compact old downtown, and Greeneville clears the one-day test for travellers who like presidential sites, Civil War borderland stories, and Appalachian town squares.
This is not a broad mountain base or a nightlife stop. Come with a history bent, give it half a day to a full day, and it will reward the detour from Johnson City or Knoxville.