New York Presbyterian Urgent Care Centers in New York, NY located at 525 E 68th St., . The hours of operation for this clinic are not known, however most walk-in clinics are open daily and for extended hours. New York Presbyterian Urgent Care Centers 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 New York in cities including NY and Hoboken.