You can jump on the Blue Ridge Parkway all the way up to where it intersects with I-64, where you have several choices from there. You can continue on the same road, which becomes Skyline Dr., and you'd be able to take it until you hit I-66E, which will lead you to Washington DC. You could also choose to take Route 50 instead of I-64, it's a bit slower and a better view. You could ride up the Blue Ridge Parkway, and leave it once you hit I-64, to jump across a bit west to Route 11, which runs parallel to I-81. Great mountain scenery on that road. Another good option is Route 29 once you hit I-64 from the Blue Ridge Parkway.
Hope that helps some!
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