Okay, so I'm a resident at NYU right now, so obviously I would know about this program more than the others. However, from what I could gather from my own experience in interviewing, word of mouth, etc, this is the summary of the programs:
- Cornell: Good fit if you're pretty much set on getting a lot of psychoanalytic type of supervision and training. I don't know if you deal with patient population that extends much outside of the Upper East Side of Manhattan (which is a pretty swanky neighborhood). Folks are proper, serious; you know, analytic.
- Mt. Sinai: Nice place to do research. Ron Rieder, who was the residency director at Columbia until a year ago, is now the residency director there, so I think the research stuff would be even more strengthened, and now they're sending their residents to NY State facilities (i.e. Manhattan Psychiatric Center), which can be a valuable experience dealing with really, really sick folks and/or patients with lots of forensic history. Hospitals covered by residents are Mt. Sinai Hospital (Upper East Side) and the Bronx VA. Don't know about how the residents are in terms of sociability, etc.
- Columbia: Said to be "the best" in NY, if not in the country. Their residents don't mind telling you this also during your interviews, which may work for or against them I guess. Eric Kandel's name is mentioned about 11 times during the day also. Anyway, it's a great place to do research. Spanish speaking skill would be a plus, since you're in Washington Heights. The mood of the residents and the faculty, overall, I thought were a little austere, maybe a bit stuffy, etc. After all, it is Columbia. (By the way, I do have supervisors and directors who were trained there, and they're pretty great, so this isn't necessarily the rule.)
- NYU: Big strength is the clinical training and public psychiatry. Research stuff is being developed, but definitely not so much as other places. If you are a "learn-by-doing" person, this is a great place. You rotate at 5 or more different sites, which includes Bellevue (where it's 90%+ involuntary pts), NYU (100% voluntary), Lenox Hill (community hospital in Upper East Side, 90% voluntary), Manhattan VA, and various State facilities. The big bragging point and the draw for the applicants is Bellevue, where you see the sickest of the sickest before anyone else may have had a chance to see them (unlike the state facilities). It's the birthplace of psychiatric emergency services (the CPEP), and you work there a lot during the first year. Basically, you become pretty solid on decision-making pretty early on in your training (i.e. whom to admit, to release, etc). It's also good if you're hardworking and self-driven. If you're looking for a laid back place, this is NOT for you. And the residents are, honestly, the most fun and social group I've seen among the places I've interviewed at, which was a huge plus for me.
Can't really say much about other programs, particularly because I really don't know much about them. But as it was pointed out by someone above, these four are probably considered the "top tier" in NYC, but as you can see they are pretty different from one another.