I recommend the book on the Blue Ridge Parkway by Rose Houk.
If it were me, I'd head west from Raleigh and get on the Parkway at Deep Gap, NC. Then I'd head north on the Parkway. Depending on your interests, and depending on how much driving you want to do each day, you might consider stopping at the Blue Ridge Music Center, just north of the NC-VA border.
If you are looking for just dry camping, right on the Parkway, there are a few options. Doughton Park, Rocky Knob, Peaks of Otter, and Otter Creek are all within what would be about a 600-mile loop, returning to Raleigh from the north. Each of these campgrounds has at least a couple of hiking trails accessible right from the campground.
-Speak