If you are traveling south on I-81 in Virginia, you can exit at Front Royal and pick up the Skyline Drive and take it all the way south to the Smokies. The Skyline Drive and Blue Ridge Parkway (heading south the Skyline Drive becomes the Blue Ridge Pkwy at Waynesboro, VA) run parallel to I-81 for awhile. The Blue Ridge Pkwy ends at US 441 near Cherokee, NC. You can then drive over the mountain to TN on US 441 into Gatlinburg. All in all, a beautiful drive (about 570 miles) but you should allot at least 3 days to do it (4 is better). Lots of stopping points and short hikes to water falls, etc. on the way. As others have said, a beautiful area to travel in the fall!
Once in the Smokies don't miss Cades Cove. If you come via the Blue Ridge Pwy, stop at the Oconaluftee Visitor Center to pickup all the information about the Great Smoky Mountains National Park. If you come via I-81 and Rt 66 & 321 into Gatlinburg, go out to the Sugarlands Visitor Center near Gatlinburg to get all the park info.