From Gatlinburg, just follow the main Parkway to the Great Smoky Mountains National Park. After you see Sugarlands Visitor Center, you can take a right on Little River Road. You stay on Little River Road which is a winding road, and often busy, for a little over 20 miles. The scenery is beautiful on your way to Cades Cove, where you will dead end.
From Townsend, go straight at the junction of Lamar Alexander Parkway and Wears V alley Road. Turn right at the "Y" junction and follow the road for 11 miles to Cades Cove.