The closest airport to Gatlinburg, TN, is McGhee Tyson, located 12 miles south of Knoxville, just over a 40-mile drive from Gatlinburg, with a few different ways to get there, depending on if you want to go to Pigeon Forge first, or take a scenic option.
You’ll want to rent a car to drive, which you can arrange at the airport.
The fastest drive is Highway 129, then east on Highway 168 which intersects with 441. This take you south towards the mountains, and into Pigeon Forge, and on to Gatlinburg.
For an alternate route, you can go south to Maryville, and then go east on Highway 321. You can continue east on different roads to intersect with 441, or to take a more scenic drive by staying on 321 to Townsend.
Highway 321 gives you options to turn south into the park, or you can take 321 through Wears Valley into Pigeon Forge.
Another option is Foothills Parkway, a hugely scenic drive that came into existence with the completion of the missing link in 2018. Access is from Walland before you get to Townsend, and take to Wears Valley, and then get back on Highway 321. You will miss the direct entrance to the national park along this route, but you can go back to that entrance from Wears Valley. The Foothills Parkway view is worth seeing at least once in your visit.
If Gatlinburg is your goal, or if you want to go into the Great Smoky Mountain National Park, from Townsend you can leave Hwy 321 and head south towards the Townsend Wye.
From the Wye, you go into Cades Cove, or head east along the Little River Road into Gatlinburg. You’ll pass through natural attractions, including Metcalf Bottoms and a chance to head up to Wears Valley through Metcalf Bottoms, or you can continue ambling east through the park to Sugarlands Visitor Center, right next door to Gatlinburg. Just follow the signs.