I did my residency in NYC. There are advantages and disadvantages, as with anything. For me, the advantages way outweighed the disadvantages.
Yeah, the ancillary staff at many hospitals isn't the best/easiest to deal with. This may or may not have anything to do with the fact that many hospitals nursing staff is unionized. But its not anything you can't get used to or learn to work around. It will require you both to hone your people skills and to toughen up.
As a resident the income won't differ too much from residents elsewhere. You will pay a lot more in rent, but the salaries are slightly higher for residents in NYC and many hospitals offer subsidized housing. I was able to even put away some savings during residency while not really limiting myself in terms of entertainment or buying stuff. Having said that, I was single at the time. The calculus may change if I had been married with kids, but I know plenty of residents who are/were married with kids and survived just fine on their resident salaries. The attending income is lower than in many parts of the country, but that is true of the North East in general. Having said that, you can make significantly more if you are willing to commute out of the city a bit. It helps to think of living in NYC as a luxury, for which you have to pay a luxury tax.
I don't know if patients are any more difficult than elsewhere. There are difficult patients everywhere. It didn't really occur to me as an issue. The patients are New Yorkers. Once again, may have to toughen up if you want to make it here
There are lots of advantages though. On your limited time off as a resident, you are a short subway ride away from the best restaurants, bars and shows in the world. The city is really amazing (if you like big cities). No other place really compares in terms of energy and the sheer mass of things going on. If you are a foodie, this place can't be beat by any other place in the world. Also, if you don't try living in NYC now, then when are you going to do it?