Within Gatlinburg itself, the best advice is to park once and walk. The main strip — US-441 — is only about two miles long, and driving it in peak season can take longer than walking. The town runs a free trolley service that covers the main corridor and several outlying areas including the Arts and Crafts Community on the east side; it runs frequently in summer and fall.
Parking is the recurring headache. There are several paid garages and surface lots off the main strip, and spaces near the park entrance fill up by mid-morning on busy days. Some visitors park at the Gatlinburg Welcome Center on US-66 and take the trolley in. If you're planning to hike in the Smokies, certain popular trailheads now require timed-entry permits during peak season — check the National Park Service website before you go.