I haven't stayed at any of these places, so can not vouch for their quality.
Brunswick - 1 mile away on Souder Rd.
Travelodge by Wyndham (website) 620 Souder Rd. 240-367-9472
Brunswick - 3 miles away off of US 340
Holiday Inn Express (website) 1501 Village Green Way. 301-969-8020
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 are several Airbnb's in the area, including a couple in town, 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).