Burnt Church Road Urgent Care in Bluffton, SC located at 1 State Road S-7-163, . The hours of operation for this clinic are not known, however most walk-in clinics are open daily and for extended hours. Burnt Church Road Urgent Care appears to be individually owned and operated and not part of a larger network of clinics. There are, however, 2 walk-in clinics within 20 miles of Bluffton in cities including Hilton Head Is. and Hilton Head Island.