The Bike Washington site has lots of info on local trails:

http://bikewashington.org

Arlington County has a good bike map showing their trails and on-road bike routes (bike lanes and other recommended streets for cycling):

http://www.bikearlington.com/pages/maps-rides/

Potomac Pedalers (http://www.potomacpedalers.org) has some trail rides, generally in the slower ride categories. They have a ride every Sunday that does a trail loop in Arlington and ends with lunch in Shirlington.

For road rides, you might be interested in the Oxon Hill club, too: http://www.ohbike.org. They generally ride in southern Maryland but many of their ride starts are not too far from here. They have a fair number of members who live in Alexandria and Arlington.