St. David's South Austin Medical Center (512) 816-7130, (512) 816-6178; St. David's Round Rock Medical Center (512) 341-6408; St. David's Georgetown Hospital (512) 942-4641; St. David's Surgical Hospital (512) 901-1173; Central Billing Office. 6000 Northwest Pkwy Suite 124 San Antonio, TX 78249. Hours: Mon - Fri: 8:00am - 5:00pm. St. David's Medical Center (866) 391 ….