We would like to have a look at the Shenandoah and Great Smokey National Parks as well - or maybe you get to see the best of them from the two roads? We are primarily looking at the scenery but would stop to look at historical sights as well.
The BRP won't give you any sort of a taste of the Smokies, or not much of one anyway. It spends a few miles in the Balsams Range, which pokes into the southeastern bit of the park, but on the whole it explores what it's named after: the Blue Ridge Mountains. The Smokies are worth many days to themselves with plenty of scenery and historic sites (mostly pioneer settlements). The North Georgia mountains and Cumberland Plateau are worth looking into as well.