I-95 to I-26 to I-77 to I-81 is a perfectly fine route, and would be what I would use by default.
For the sake of variety, I've also done I-75 to I-40 to I-81. That's a little longer, from Stuart about a couple hundred miles more (it's less of a difference from the Gulf Coast where I more frequently have gone), and you do have to deal with Atlanta. If you want to stop at the Gatlinburg/Pigeon forge area, then it's a great option.
If you have all the time in the world, going up the Blue Ridge Parkway/Skyline Drive is a beautiful but slow option.