Greeneville Tennessee Traffic 2024-12-01 Roadnow Weather | Gas | Restaurants | Hotels | Car Repair | Convenience Stores Cities close to Greeneville Tennessee Mosheim, TN 13.76 mi Afton, TN 16.17 mi Midway, TN 16.41 miInterstate highway exits close to Greeneville Tennessee Exit 30, i81 20.04 mi Exit 23, i81 21.51 mi Exit 36, i81 24.69 miInterstate highways close to Greeneville Tennessee i81 map 20.04 mi i26 map 29.45 mi i40 map 35.78 miState roads close to Greeneville Tennessee TN 70 map 1.32 mi TN 351 map 4.06 mi US 321 TN map 4.35 mi