The only NYC programs I would seriously consider are Cornell, Sinai, and Columbia in that order.
Columbia was great many years ago, but has faded since. You spend up to two hours per day babysitting patients in the or when the case is done because the pacu is full, etc. (inner city hospital issues). None of this wasted time at the other two programs which translates into same caseload but better hours. Also the atmosphere at Columbia isn't that great. Residents don't spend much time together, nursing isn't the best, not much teaching, and collegiality with attendings could be better. I had just heard too many complaints from residents, and too many comments from program directors about Columbia losing it's edge, to rank this program highly.
Sinai rocks, but lacks a national reputation. This makes you less competitive for fellowships and out of state jobs. Otherwise the atmosphere is great, mostly because of the program director. Perks are good as well, free lunches every day and if lucky you can get semi-subsidized housing (still expensive and not guaranteed). Diverse caseload (biggest weakness is pain) and probably the best didactics of the three. Trauma rotation is done at a hospital in Queens and pain is at the Bronx VA.
Cornell has it all in my opinion. Contrary to what has been posted, the caseload is extremely diverse. Like Columbia, minimal trauma. And yes, Sinai has liver transplants (New York Hospital does have a transplant program, just not livers). But an integral part of the program involves two of the best specialty hospitals in the country-HSS and Sloan Kettering. These places do surgeries that other hospitals in the country won't do. Not to mention the great caseload at NY Hospital. You have exposure to the spectrum of anesthetic techniques, amazing regional and pain, and the reputation to boot. Didactics are very good, but probably not as good as Sinai, definitely better than Columbia. Also, the residents are extremely happy. I would be too if I got to live on the Upper East Side in sweet apartments at a fraction of the retail cost. And the best part of it all, call from home. That means that when your last case is done when you are on call, you go home and only come back in if needed. It's a beautiful thing.
I ranked Cornell first but didn't match there (happy with Stanford, number two).