Dickson-Williams Mansion is an 1820s historic house near downtown, usually visited by guided tour. Its appeal is not just the furniture and Federal-era architecture, but the way the house sits inside Greeneville's Civil War and political history: local elites, soldiers, and visiting politicians all passed through rooms like these.
Check tour times before building a day around it. When open, it gives Greeneville's history a domestic scale after the larger Andrew Johnson story.