Billy Goat trail is awesome! The trail is actually on the C&O Canal and rims the Potomac river. It has a moderate to difficult climb, though you can choose which section of the three to hike. You can go 1 - 3 or even 5 miles on it! What is cool is that along the trail is the Potomac river and at times while you are bouldering on cliffs overlooking the Potomac, you can see on the opposite side, climbers on the Great Falls, Va side.
The whole loop is about 5 miles, and you can bring your dogs too, the terrain is rocky, so bring your hiking shoes!
Directions:
The Old Angler's Inn is a place to start. Right off the Clara Barton Parkway.