While scheduled at the Center for Specialized Medicine (CSM) on South Grand, visitors may park in the Hickory East Garage. The address of the garage is: 3424 Hickory St, St. Louis, MO 63104. The garage is located across from the CSM on South Grand. You can see that garage on the map in red/orange. The CSM is #18 so you'll have a few blocks to walk to get complimentary parking.
The hospital garage which is attached to the CSM is an option, but it is not recommended. Parking is not free (with a validated ticket it's $2/day) and parking can be limited in there since it's typically reserved for patients.