Up I-95 with a stop in Savannah, we love Savannah, then on to I-26 to I-40. Getting off 40 at exit 27 on to 23/74, then onto 19 through Maggie Valley to crossover the Park on 441 going into Gatlinburg. A stop in Cherokee is OK, if you've never been there but tighten up the purse strings. The ride through the Park on 441 can be very slow, but very scenic. If short on time, I'd continue North on I-40 until you hit 321, hang a left. You can always do 441 after visiting Gatlinburg and Pigeon Forge(Dollywood). This is what we do when visiting DW's cousin in TN. albeit not during winter time.
Jan and Bob