I haven't stayed at any of these places, so can not vouch for their quality.
Brunswick
Green Country Inn
620 Souder Rd.
301-834-9151
Knoxville - 5 miles away, west on US 340
Hillside Hotel
19105 Keep Tryst Rd.
301-834-8144
Jefferson - 5 miles away, north on US 340
Jefferson Motel
4029 Jefferson Pike
301-473-5711
Lucketts - 10 miles away, south on US 15
Little Rock Motel
14880 James Monroe Hwy. (US 15)
703-777-3499
There are also many places in Harpers Ferry, WV (10 miles away), Frederick, MD (15 miles away), and Leesburg, VA (15 miles away).
For some cheaper alternatives there is a hostel in Knoxville (Harpers Ferry AYH Hostel, Sandyhook Rd., 301-834-7652, on the Appalachian Trail) and a campground in Brunswick (Brunswick Family Campground, C & O Towpath, 301-834-8050).