Welcome to Virgina.
Loudon is a great place to ride. Lots of quiet, and not so quiet, country roads. Good riding in Faquier, too.
I've never ridden around south riding so I don't know what is at your door. Maybe Braddock Road and Gum Springs.
One good loop from Middleburg involves Sam-Fred Rd out and St Louis back, then Atoka out and Zula back. That's not too far a drive for you
Mid-county is Lincoln Rd, North Fork, Snickersville, Airmont, Silicott Springs.
Up-county is Woodgrove, Mountain Rd, Irish Corner, Taylortown, Milltown, Loyalty, Clarksburg Gap
East-county is the W&OD, Harmony Church, Woodburn, and lots of riding around Landsdown, Ashburn and Sterling.
And west-county is Mount Weather
PPTC does a lot of rides in Loudon. Try one of their club rides, or join to get access to their cue sheet library.
One of their regular rides is a loop around Dulles Airport. Probably uses the Loudon County Parkway and Old Ox Rd.