East Garage 1210 Medical Center Dr. (22nd Ave S) Nashville, TN 37212 The East Garage entrance is located on Medical Center Drive across from the hospital. The Valet Parking Entrance is located on 21st Avenue, next to the Medical Arts building. Valet hours are 5:00 a.m. – 7:00 p.m. Visitors coming to Medical Center East: Once you have parked in the garage, look for the elevators in the garage. These elevators take you to Medical Center East floors.