Does it need to be paved?
Capitol Crescent from Georgetown to Bethesda, then combine it with the Rock Creek Trail / Beach Drive back to Georgetown. 21 mile loop. Popular, so it can get crowded.
Or Rock Creek Trail / Beach Drive from end to end. 50ish miles from Georgetown to Rockville. The upper trail is less trafficked and Lake Needwood makes a nice turnaround.
One of my favorites is the North Central / York Heritage Trail. Timmonium to York. Not paved but in good shape.
The Maryland section above Whitehall is very remote and quiet. The PA section still has the train tracks (mostly inactive) and goes thru several towns.
On the VA side, W&OD, Alexandria to Purcellville. 90 mile r/t.
Or Mount Vernon Trail along the river. 38 mile r/t.
This might help
http://bikewashington.org/trails/rtrails.htm