One of the most scenic highways in Virginia is US 250, which crosses eight mountain gaps on the way to the W Va border. It is the highest normal US highway in the East north of North Carolina-TN (where US 441 is over 5100 feet in spots). There are plenty of hairpin turns, and the last approach to the divide above Monterey takes forever. There are no tunnels to my knowledge.
Along US 250 at Shenandoah Mountain gap, about 3300 feet
Allegheny Mountain, on W Va border, 4330 feet on highway, about 4500 on surrounding peaks; there is a nice home and property on the border at 4500 feet maybe a quarter mile off the road; a lot of land is privately owned despite National Forest. This is also the Eastern Continental Divide; the same mountain formation houses the Allegheny Mountain tunnel on the PA Turnpike 150 miles to the north. Climate is Canadian in winter, like going 600 miles north. Elevation matters more in eastern US than in the Rockies. The same mountain also produces Spruce Knob about 30 miles to the north.
Spruce Knob Mountain Center, on dirt road from W Va 28, I think at about 4000 feet; the peak is off in the distance
Shenandoah Mountain on US 33 west of Harrisonburg, very steep road although elevation not so high (about 3500 at gap)
(Published: Saturday, June 18, 2016 at 10 AM EDT)