Hi Kristina -
You may have already found this but there are threads in the NY State Nursing Programs forum specifically about the NYU program; the one for fall 2013 applicants is here: http://allnurses.com/new-york-state/...ll-810051.html
I just completed NYU's accelerated program in December and overall really enjoyed the program. There are some downsides for sure, but I imagine that is true of any program. I felt the instructors were excellent and the clinical opportunities were good. For anyone I'd recommend being very active in their clinical experience and trying to make the most of it that you can. The instructors are there to help and facilitate your learning, but they can't know exactly what each student wants if you don't speak up.
I'm just now beginning my job search so can't speak to how desirable the NYU degree is to potential employers...check back in a few months on that! I'd imagine that the NYU degree would be well received by graduate programs.
Finding pet-friendly apartments in the city can be challenging - I have pets and the options were limited when I first started looking. I live in Queens, which I found to be much more affordable than most places in Manhattan; the same is true of areas in Brooklyn and either wouldn't be a terrible commute to NYU depending on where you were.
If you have any other specific questions I'm happy to answer if I can. Good luck!