i took a route recommended to me by one of the Rangers which differs slightly from the maps.

You'll want to start at the Backpackers lot near Massie Gap, Take the Rhododendron trail northbound until it intersects with the Horse trail. Keep going north until it meets the AT going northbound toward mount Rogers. The whole stretch is a bit of a hike but I'm sure you'll see them pretty early on.
It's about 6 miles to mount Rogers from the lot but the scenery is well worth it. Huge meadows, vast vistas above the valley. Very magical! Also, If you decide to hike out of the park and onto the AT, there's a herd of longhorn bulls that graze on the federal land. There's like 30-40 of them. Kind of scary if you aren't expecting to run into them, but worth a few photos for sure.