Good call by Steelisreal. Big South Fork on the Tennessee/Kentucky border would be awesome. Lots of trail and dirt road with the river running through the middle of it. I think starting in Tn and riding up into Ky then rafting back would be fantastic. The route I have planned would take 2 days minimum and that is without rafting, so I don't think you would have any problem making it three+ day trip.
Most of the Virginia section is going to be pretty burly singletrack so I wouldnt recomend a cross bike. Honestly, the whole southern end with the exception of the New River trail would be unrideable on one.