Hi Joyce,
I had my GK at NYU and they will valet park for you. Whichever big hospital you go to will usually do the same. Not cheap for sure, but nothing is in NY. I would check with the hospital before you go (they might have a concierge service). Sometimes you have to be there so early, the valet is not available. If you will be staying at a hotel the night before, you could probably park nearby there (check with them as well) and take a cab over. Hospital can usually provide names of nearby hotels, and sometimes have special rates. Hotel can tell you about parking there and getting cabs. Sounds like a lot, but once you know what you are dealing with and set it up, it really is not bad. I had about an hour or so drive home afterward, and really had no problem. A little sleepy, but that was it. Good luck.
Best to you,
NYL.