I love riding the Parkway; the only place I've ever had a concern about drivers is in the Asheville area where a part of it is used as a local shortcut. Of course having shared the road with motor vehicles for 50 years I've developed a tolerance.
As I remember the Parkway in that area it's pretty gentle - rolling hills through farms and orchards. It starts to get more challenging as you approach Roanoke.
I rode the New River on 32s. I think you could ride it on 23s because as someone noted it is firmly packed. It has been about 15 years since I last visited and conditions may have changed. Great ride though and the camping facilities are good.
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