We just stayed at the Hyatt a couple weeks ago. Valet parking was $13.00 ($18.00 minus a $5.00 discount for staying at Hyatt).
There was a cheaper option by parking in the airport garage, but the closer parking garage was closed due to the high terrorist alert. We didn't want to bother with dragging our luggage across a parking garage and through the airport, so I didn't even ask how much the parking was at the airport garage that was further away. Now that the terrorist alert has been lowered again, maybe you can park in the nearer garage.
I called the Hyatt before my stay and they answered all my questions.