As it has been suggested Mount Rogers is a great place to go. It was the first place that I went on an overnight backpacking trip when I was 8, so I am especially fond of the area. If you decide to go in August, there are “millions” of wild blueberries on the trails. My favorite trails up that way are the AT/Pine Mountain Loop (10-11 miles) and gives one a good work out.
My other favorite place is the AT on Roan Mountain. Park at Carvers Gap (5512’) and hike over several balds all above 5000’, with outstanding views on a clear day. One time when I was there, I could see all the way to the Smoky Mountains! After the balds, begin a long descent down to the “barn” shelter. This makes for a good place to camp or spend the night in the shelter. Next day, you are greeted by a 900’ climb in 1.8 miles, but the view from Little Hump Mountain is worth it. Continue on the trail until you begin to climb the 400 acre and 5587’ bald. Once again 360 degree views await at the top and makes the climb well worth the effort in getting there.
I fell in love with both Rogers and Roan while in school at Appalachian. Much of my free time was spent in both areas and whenever my friends would ask where I was going, I would say “Roaming Roan or Rogers”. Enjoy your hike.
Trekking Trav