How far do you want to go? How far are you willing to drive for a starting point?

The Crescent trail is pretty short, but it links up with other trails at the Georgetown end (Custis and Mount Vernon) and also links with the Rock Creek Trail in Maryland.

This site might help you:

http://bikewashington.org/trails/index.htm

For the WOD in particular, there is also: http://www.wodfriends.org/

The eastern part of the WOD has more at-grade crossings and tends to be more crowded (although during a weekday in the rain crowds should not be a problem). I drive out to Reston Town Center and ride west from there when I want longer stretches without having to stop. There's lots of parking in Reston.