Live in Falls Church, work at Fairfax Circle. Been ridin' 'round here for more the 20 years.
You've got lots of choices of routes. Where do you want to go? How much riding do you want to do?
Bradock Road out to
Old Centerville Road (stay off the other one) gets you to Manassas (twahl country) and points beyond. If you throw in Prince William Parkway and route 123 you've got a 40 mile loop.
Old Lee Highway or Picket Road get you to the Farifax Connector Trail and the W&OD at the Vienna Community Center.
From the VCC there are some good routes to Great Falls, although these are probably best on weekend mornings.
Route 50 at Nutley Street is one end of a trail that takes you past Wakefield and around Lake Accotink. From there you can keep on going on the CCT to Mount Vernon if you want to.
There's a hilly route of neighborhood streets that zigzags from Fairfax City to Annandale and Arlington (I think I can find the cue sheet again.)
Lots of ride options in Arlington, Alexandria and DC. Falls Chruch to Rockville is one I like.
And there's some fine riding out in Loudon, past Leesburg and Purcellville. Or in PW past Manassas, around Nokesville and Catlet.
This site is a good start.
http://bikewashington.org/
and the PPTC has a cue sheet library.