I know cornell has a few undergrads...I think Columbia as well...in the ED doing filing or some scribe stuff. I just remember seeing them when I used to bring patients as an EMT.
However, you are going to find it to be VERY hard to find undergrad experience in these places unless you have someone on the inside.
They are just simply too busy to accommodate people asking to do anything hands on. They will probably give you some candy-striper job through the volunteering dept...if that even exists. It probably doesn't at places like Monte, Jacobi, Bronx Leb, anything in Queens, Brooklyn, and most manhattan hospitals. The nicer hospitals probably have some volunteering office. The nasty ones don't really care/have use for anyone who doesn't speak another language. If you DO speak spanish/chinese/korean then you probably may be able to find something. I know we are hard pressed to find people like that sometimes.
I would try community hospitals outside NYC...why the attraction to NYC? Do you live there?