We made AMS our last stop and dropped the car before we hit the city. I do know that Hotel Pulitzer has valet, but I'm sure it is expensive as it would be at any of the other major hotels.
Anyway to leave the car at your previous stop or outside the city and take a train in?
I also had no desire to drive in Amsterdam. I would have ended up in the tram lane!!
Three years ago we parked in the parking garage at the Heineken Brewery which is pretty central (you can walk to downtown or take the tram). Id on't recall the exact pricing but it was reasonable.
I just posted the following last week:
I've been fortunate to take two business trips to northern Germany (Dusseldorf, Cologne, Aachen and Alfeld) over the past couple of months, and I just flew out of Amsterdam on Sunday. If you intend to drive in the city center of Amsterdam, I would urge you to avoid peak traffic times. Between the narrow streets, canals, street cars, cars, mopeds and TENS of THOUSANDS of bicycles and pedestrians.... it made driving in Italy seem like a country outing. I was in a rental car, but if I was driving my own ED BMW, I would have been quite nervous.
My advice is to do what others have suggested - park outside of the city and take the train in.