I went to NYU for my BA...it's an excellent school, but it's a very expensive one. When I was an undergrad it was about 14-18k/yr--I had scholarships
and financial aid but I still paid a good chunk out of pocket. Now I hear it's about 30k/year.
I don't know what your financial situation is like, but for 30k/year, you should be fairly
certain of what you want to study...though keep in mind that freshman year won't throw you right into the nursing/medicine fire, but instead you will be ticking off a lot of Liberal Arts requirements and pre-req science courses. Also, many students change their minds about what they want to do that year and even in their sophomore year, because they get exposed to all of these new subjects that they wouldn't have thought of. You could start and if you decide you don't want to do nursing, you could always transfer into the College of Arts & Sciences/Tisch/Gallatin/whatever.
But remember, you're paying 30k/yr. So if you have any serious doubts about NYU, perhaps it's best to go to a CC for a year or two first, and save that money. You could always transfer in later.
And like others have said, having gone to a school like NYU doesn't always give you an automatic edge to your career. I'm living proof