Shannon Medical Center 120 E. Harris Ave. San Angelo, TX 76903 Phone: 325.653.6741 Map and Driving Directions. Shannon Clinic 120 E. Beauregard Ave. San Angelo, TX 76903 Phone: 325.658.1511 Map and Driving Directions. To email a question or comment directly to one of our departments, please select the appropriate link below: Medical Records ....