Are you looking for road only or road and dirt? If you include gravel paths, you could take the C&O Canal path from Georgetown to near Leesburg, VA and then work your way south. It's a long way from Georgetown to Front Royal - probably about 100 miles or more. I've ridden it from Fairfax (near Chantilly) to Front Royal and it is about a 80 mile ride. Here is a basic route - let me know if you want more details.
Starting at Key Bridge in Georgetown
Go across Key Bridge to Arlington, turn right on Custis Trail which starts in Virginia at the end of the bridge by Key Bridge Marriot
Heading west on Custis Trail until you merge onto W&OD Trail heading west.
Continue on W&OD Trail to Herndon
There are several roads south to Route 606 continuing on south until you reach Route 29
head south on Route 29 through Manassas National Battlefield
continue until you reach Gainesville and turn onto Route 55 West
Route 55 parallels Route 66 all the way to Front Royal
Route 55 is a great road since it is easy to follow with only moderate traffic; the heavy traffic is all on route 66.