First, check out http://www.nukefix.org/parkway/
if you're willing to stay on the Parkway.
There aren't a lot of good parallel routes for a fair bit of North Carolina, IMHO. Around Boone, for example, stay on the BRP from Deep Gap to Linville, if possible. There are local roads, but the ones paralleling the Parkway typically have no shoulders and heavy, high speed traffic. U.S. 221 traffic from Linville to Linville Falls is variable, and it's scenic, but it's narrow and winding -- no good sight lines.
Likewise, from NC 80 to Asheville, I'd stay on the BRP. There's no good, close parallel. I-40 has to climb over the Blue Ridge, and swallows up U.S. 70 on the south. Don't know if the opening of I-26 has helped U.S. 19 on the north, which used to be narrow, winding, and heavily trafficed.
There's some local clubs and riders in Asheville who might be able to help with alternate approaches, if you're intent on getting off the BRP. But for my tastes, it's a beautiful ride from Little Switzerland up toward Mt. Mitchell, and a heck of a downhill from there! Just make sure you have lights, as there are tunnels from Little Switzerland all the way down to Cherokee.