Property Location Located in Greeneville, Hampton Inn Greeneville is in a rural location, a 3-minute drive from Greeneville Community Hospital East and 6 minutes from Niswonger Performing Arts Center. This hotel is 3.6 mi (5.9 km) from Simpson Island and 3.8 mi (6.1 km) from Lost Island. Distances are displayed to the nearest 0.1 mile and kilometer.