There’s a Reddit group called r/dmvbikepackers that plans weekend bikepacking/bike touring outings on the C&O canal. The canal connects to the Great Allegheny Passage, which goes all the way to Pittsburgh. You do need the right equipment for this, however. (Bikepacking bags or racks and panniers, ultralighting equipment instead of car camping equipment, etc.). The C&O and connecting Great Allegheny Passage are nationally famous for bikepacking. Other than that, Appalachian Trail, Shenandoah National Park, and Assateague Island are all also famous, local camping/outdoors destinations.