Since you plan to include Asheville – then I would strongly recommend Chimney Rock Park if it is not already on your itinerary.
A few years ago I took fly-drive to that part of the States (in and out of Washing DC), heading as far south as Savannah.
I can’t say that it is the most exciting/interesting part of the USA.
Washing DC is worth a couple of days looking around, Memphis is only worth visiting if you must see Graceland.
My Walmart Rand McNally Atlas recommends the scenic route of Highway 12 along the coast of North Carolina.
My advice would be to check out Trip Advisor for what is on offer in the towns/cities close by and choose your route accordingly.
With regards accommodation, personally I would advise planning your itinerary – and booking the hotels before you go (you can get some very good deals on expedia etc.), otherwise you may find you are paying top whack for your night’s sleep.