There is valet parking and self-parking. You pay for both. Valet is right at the lobby door and if you want to self park, you drop your luggage off at the lobby and then park in the lot below. There is a very long flight of stairs to go from the parking lot to the hotel.
For fairness to those not parking, only those with cars are charged a parking fee. I believe it is $6 (may have gone up) per night for self-park. Valet is about twice that amount.