I did a little "research" (read: Googling) and what I found was that you can file for an appeal if:
1. There have been changes to your resume, scores, etc., or there are large, positive changes. So, any revisions that would change the rigor of your application, and
2. There is a clerical error in your application, such as a misprint on a transcript.
There were several reasons listed that were considered "unacceptable" for filing an appeal, including 1) feeling the decision is incorrect or unfair, 2) feeling like your grades were good enough, 3) you've gotten in to other, similar programs, 4) you know people who have gotten in and that have similar credentials as yourself, etc.,
Of course, every school is different, but these seemed to be the common theme that came across when I looked into it.
NYU in general (undergrad) does not really entertain appeals:
We do not have an appeal process of any kind and we cannot reconsider your application before May 1. If we are ultimately not able to offer you admission after May 1, you can certainly re-apply for admission as a transfer candidate to our campus in New York, should you matriculate elsewhere next fall, but we cannot reconsider your application until then and we cannot evaluate any new credentials or materials at this time.
The appeal processes I found for NYU involved current students and revolved around contesting grades, leaves of absences, dismissals, etc.,