Definitley agree with @BatmanTheElf  - riding to DC via the C&O is a low stress, low logistical bikepacking trip. 

The W&OD is also great - start in Georgetown on the Custis trail towards Arlington and it connects all the way out to Purcellville, VA. Even better, you can make a loop from DC to Leesburg, VA via the W&OD, then take the Ferry at White's Ferry back into Maryland and connect to Rock Creek back down to the city. 

Despite the traffic, politics, crowds, etc. DC is one of the best biking areas I've ever lived!