Tully Health Center - Immediate Care Center Services The Tully Health Center is a comprehensive healthcare facility located at 32 Strawberry Hill Court, Stamford, Connecticut. It is part of the Stamford Health system and offers a wide range of outpatient services, medical treatments, and wellness programs. As a modern medical hub, Tully Health Center is known for its patient-centered care and its state-of-the-art equipment, which allows for the...