Branson Allergy Clinic Address 525 Branson Landing Blvd Branson, MO 65616 location Get Directions Phone: 417-348-8080 Hours This clinic is open every Wednesday. About Cox Medical Center Branson is a full-service hospital caring for residents of and visitors to Stone and Taney counties. From our newly expanded and renovated Emergency Room and critical care areas, to our new Women’s Center, Cox Medical Center Branson offers the care you need, right here.