I don't know much about fishing but here are a few ideas.
1. The AT near Lexington VA. Check out the secion throught the James River Face wilderness and the north of the James River to the Blue Ridge Parkway. Good scenery, and one of the bigger wilderness area in VA. Check out Devil's Marbleyard.
2. St. Mary's Wilderness is supposed to be good, haven't tried it yet.
3. Grayson Highlands area. This is very scenic, go in the fall or spring when its not as crowded and you can experience some real mountain weather.
I just remembered another section of the AT. Check out Tar Jack Ridge and Cold (also know as Cole) Mountain north of Highway 60. Its not as remote but the views are great.