I second the suggestion of Sky Meadows State Park. It's very nice, but IIRC there is an admission charge at least on weekends.
It's unclear how far you're willing to walk and how far you want to drive to get to the hike.
Catoctin Mountain Park and nearby Cunningham Falls State Park in Maryland near Thurmont, MD have some nice hikes.
George Washington National Forrest just over an hour west of Fairfax has nice hikes and no admission charge.
Shenandoah National Park has some of the best hikes in the area, but there is an admission charge and Skyline Drive, which runs the length of the park, often has a lot of traffic. Some trails are crowded in good weather, but after you get 1/8 of a mile off Skyline Drive the number of hikers drops dramatically on most all trails.
Below are some websites that list numerous other hikes.
http://www.midatlantichikes.com/
http://www.hikingupward.com/
http://www.trails.com/
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