three days in northern Virginia, West Virginia or Southern Ohio

The New River Gorge and bridge near Summersville, WVA is worth a visit.I founf US 50 to be scenic but slow. Of course if you go through Southern PA you can visit the Gettysburg Battlefield Park.
Or, drop south to Lexington and hit White Sulpher Springs in WVA before deciding to take US 60 or the WVA Turnpike to Charleston.

You could go west along the C &O canal, stop at great falls of the Potomac NP, go to Harper's Ferry, take the national park service shuttle from the visitor's center, hike across the river there. Then head up to Gettysburg etc as boom-boom said.

A few... in Ohio. We have been to both several times.

http://www.thewilds.org/

http://www.roscoevillage.com/

http://www.hockinghills.com/ This is just off 50 in SE Ohio, & appears to be what you are looking for. Several posts on here if you search 'Hocking Hills' also.

Rte 50 is the lesser of the routes across the mountains, IMO, but it's scenic enough. Very windy and slow in parts. If you take it, there is a scenic train ride that runs from Romney, WV that might be worth your while.

http://www.potomaceagle.info/

About 50 miles further is Cathedral State Park. Good place to stop for a short walk amongst some very large hemlock trees.

That said, the southern Rte to Cincy (Thru Charleston WV) is infinitely more scenic, though. A cabin at Watoga State Park for a couple nights might work. Or anything in that general vicinity. Plenty to see and do in this area (Monongahela National Forest, spectacular scenery). Then check out the new River Gorge (cross the bridge on Rte 19) on the way to Huntington WV, where you'd pick up Rte 52 in Huntington WV and follow along the banks of the Ohio River right up to Cincy.

I'd take this route vs Rte 50 any day.

If you go to Hocking Hills, there are state park cabins, and the Inn at Cedar Falls is very nice. There are some beautiful hiking trails that make you feel like you are somewhere other than Ohio. If you want a more luxurious experience, you could try the Homestead in Virginia or the Greenbriar in W.V.

weimarer,thanks for the alternative route ideas. Thanks everyone for all your ideas!

If we take the southern route to Cincy,as you suggest, what highway do we take westward from DC?

you could hit Fallingwater in PA if you haven't been there before! Nearby resort is worth a visit. It wouldn't be too far off the main highway and then a scenic drive down to MD/WV border near the Cumberland

http://www.fallingwater.org/19/

Nemacolin is nice for the $$$ or more budget friendly Seven Springs

I've met a few people who were driving from the D.C. area to southern Ohio. They stopped at Avalon Resort in West Virginia.

Once, I drove west route 50 across WV to get to I-79. I thought it would never end. Every 10th of a mile or so you'd see a sign saying there was a 10-mph or 15-mph turn ahead. No way to anticipate which way the turn went until you were upon it. It took forever. Go another way.

Harper's Ferry would be a good stop. The sesquicentennial of John Brown's raid is Oct 16-19. Good article in Smithsonian mag about it.