Carilion Clinic Neurology - Franklin is located at 1171 Franklin St. Rocky Mount, VA 24151 United States, open Monday-Friday 8:00 AM to 4:30 PM |. Carilion Clinic Family Medicine - Dayton is located at 15 Killdeer Lane Dayton, VA 22821 United States, open Monday-Friday 8:00 AM to 5:00 PM |.