I just moved to New York last September. I've been a nurse since 2007. Last spring/summer I attempted whole-heartedly to get travel nursing assignments in New York, with no luck at all. In a dire attempt to move to New York, I opened my mind a bit when I found a job on craigslist for a pediatric private duty nurse. At first, I thought I would never work home care, but I actually really enjoy my job. It's fine for now, but eventually, I would like to go back to the hospital.
Manhattan is super expensive to live in. It's often easier on your pocketbook if you can get a roommate. I haven't been to the Bronx, but I definitely am pro-brooklyn as a great place to live. It seems as though getting to Queens from Brooklyn though is a hassle, unless you are driving. And as for Staten Island, I haven't been there, but I never hear fantastic things about it.
If you are really serious about moving to New York City, it may help to broaden your perspective on what kind of job you should take. There are jobs out there, but they may not be #1 on your list. That might change if moving to New York is #1 on your list.
I am at a transition point in my life, and eventually I will get back into the hospital when the timing is right. Moving to New York City was something I felt I had to do (I had been planning for a long time), and I did it.
You also need to get a New York State nursing license, so try to initiate that process before applying to jobs! It also helps if you have BSN... most job postings I see require that the applicant has a BSN.
Good lucky =)