Valet parking at the Hyatt Centric parks cars at the First Presbyterian Church - Lot #263, a block behind the hotel. You can self park at the same lot for a fraction of what the hotel charges. I paid $8.50 to park there overnight Friday night, entered at 6pm and out at 2:30 Saturday. The hotel would have charged $75 ($55+ $20 late checkout charge)
It is underground, secured and locked overnight
Amazing tip, this will save me so much money on my next trip.