I commute to NY and have my own parking garage space on Park Ave i pay monthly.
Like every other parking garage in the city, 80% of cars in my parking garages are all high-end, from Porsches to 430s and 458s and bently. These owners bring their own bumper guards, front and rear and even sides. No matter what they say and what they claim to cover, parking garages will NOT be responsible for any damage they make, and they do make some serious damages.
To put it short, even if some garages are "known" to be good, don't trust them. You never know WHO will end up parking your car, or WHO will be moving around your car, if your car will be sent up to the roof floor via elevator, etc.
If you HAVE to bring the car into the city, my best advice is to go to a "big" parking garage, tip them 5~10 bucks separately and park it in the front and NOT send the car "inside" the garage or upstairs/downstairs. Parking "front" usually means parking right by the pay-box office or the pay-machine. It is safe because your car will most likely stay there and also because the car's right by the worker's office. Some parking garage lets you just take the key if you park there. I did this several times in NYC and Boston.