Paul,
Wish we were here: you could roll up the Mtn and camp here
on the way...alas, we will have migrated south by then.
Fort St. Juan's mansion is a great stop, (since he already
invited you

).
Biltmore is worth a halfish day, if you have time. One
cannot "do it" in an hour or two.
The BRPkway is kick azz, but probably out of your way
and one cannot make time on that road, regardless of
vehicle. Some links below, for your perusal.
S'Burg/Greenville have absolutely nothing in store for
the tourist, imo.
Congrats on the Delivery.
BR,mD
Blue Ridge Parkway:
http://www.blueridgeparkway.org/
Biltmore Estate:
http://www.biltmoreestate.com/
Grove Park Inn - Asheville, NC:
http://www.groveparkinn.com/
Spartanburg,SC ...sorta like a trip to anywhere, USA:
http://www.spartanburg.com/