I think NYC is a great place to live, but it's not for everyone. Housing is expensive, which is probably what most people are turned off by, so you will most likely end up living in a smallish apartment, but there are so many other things to do, so for me, that makes up for it.
I work as a social worker at NYPH/Cornell which is on the east side (68th and York) of Manhattan. I'm in nursing school now, so when I graduate, that is where I want to work. The nurses I have spoken to like it there, and compared to the other hospitals I have worked at, the staff overall seem very professional and courteous. There is also Columbia Presbyterian which is on the upper westside (168th St) of Manhattan, so make sure you distinguish the two. I can't commnet on Mt. Sinai or Maimonides in terms of what the hospitals are like, but Maimonides I believe is southeast of Prospect Park in Brooklyn, so if you plan on living in Brooklyn, the commute there might be easier. Of course, it also depends on where you live in Brooklyn.
I live near Columbia University, which is on the upper west side of Manhattan, and I commute to the Flatbush area in Brooklyn for school. The commute is rather easy since I only take two trains. My commute time around 7:30 - 8:00 a.m. to get to my 9:00 a.m. class is about an hour. Some days longer if there are problems with the trains. Figure out what neighborhoods you want to live in and than compare to the hospitals you want to work at to see if it makes sense.
Hope this helps some!