Great Smoky Mountains National Park is the most visited national park in the country, and its traffic is distributed about as unevenly as traffic can be. The Gatlinburg and Pigeon Forge corridor takes the overwhelming majority of it. Everything else stays comparatively quiet, including in October.
Here is how the alternatives actually compare once you are driving them rather than reading about them.
Townsend, Tennessee. The closest thing to a quiet base on the Tennessee side, sitting at the Cades Cove entrance. It markets itself as the peaceful alternative and mostly still is, though Cades Cove Loop Road has its own traffic problem that has nothing to do with where you slept.
Bryson City, North Carolina. A genuine small town with a functioning downtown, close to Deep Creek and to the quieter southern trailheads. Drive times to the marquee Tennessee-side hikes run longer, and in exchange you are not paying rates set against a theme park.
Waynesville and Maggie Valley, North Carolina. More lodging, more range, a longer drive to the park. Waynesville has the better evening; Maggie Valley has the better price.
Cherokee, North Carolina. Right at the Oconaluftee entrance, which puts you closer to the Blue Ridge Parkway than anywhere else on this list.
The number that should decide this for you is not distance to the park boundary. It is drive time to the specific trailheads you intend to use, which can differ by ninety minutes between two towns that look equally close on a map.
The finished guide will run those drive times as a table, measured rather than estimated, along with what each base costs in a normal week and in the second half of October.