Gatlinburg is a driving destination. The nearest commercial airport is McGhee Tyson Airport (TYS) in Knoxville, about 45 miles away — typically a 50-minute drive under normal conditions, longer during peak weekends when the approach roads back up. Nashville is about three hours by highway.
There is no train service and no meaningful bus service to Gatlinburg. You need a car. US-441 (known locally as the Parkway) is the main route through town and the same road that enters Great Smoky Mountains National Park — traffic on this road in summer and fall can be brutal, particularly on weekend afternoons. Arriving on a Thursday evening or a weekday morning makes a significant difference.