Einstein is strong, as are a bunch of the NYC programs. As is probably obvious, no place in the country rivals NYC when it comes to the depth of the faculty and residents.
Having said that, each of the programs has its own flavor. An excellent training can be had at a bunch of them. Even the programs that are clearly second tier will have solid faculty, and, if you are attentive and work hard, they will get you excellent jobs afterwards.
Having said that, here are some stereotypes:
Columbia sees itself as the best program.
Cornell does, too.
NYU and Mt. Sinai both say that they are up and coming, and, while they've been saying that for 20 years, there probably is a reputation gap between the 2 New York Presbyterian Hospitals and the rest.
Einstein worries about being in the Bronx, but their school and program is filled with cool, thoughtful people.
More stereotypes
Columbia is all research (plenty of their trainees go into private practice). Their trainees are unhappy (seemed pretty happy) and snotty (I didn't think so). The neighborhgood is dangerous (it is a rough spot, but I think a lot of people commute from the upper west side).
Cornell is all psychoanalysis (their chair is a neuroscientist, 4 of their pgy 2's are hard science MD-PhD's; and most of their trainees don't go into analytic training; several do each year, however, and if you don't like psychotherapy, it's a bad pick). Their trainees all went to Ivy League schools (fairly true). Their patients are rich white people (most of their patients are medicare/medicaid, and, being New York, most are either non white or grew up speaking another language--ironically, it probably has the MOST diverse pt population in NYC). They have great housing (true). It's very upper east sidish (most of their faculty actually work at the Westchester division).
Mt. Sinai is about to go bankrupt (couldn't tell; may be true). They have a chip on their shoulder (may be true. Even though they're very good, they are probably fourth in the Manhattan hierarchy, and they hate it).
NYU is Bellevue (they do rotations at several places). NYU is disorganized (it is very big and much more spread out than some place like Cornell). NYU is cool (it did seem fairly laid back in a busy sort of way).
I didn't look at the others, but I have heard good things about St. Vincent's, Cabrini, and BI, though my take is that many of their residents are either international grads or less driven by medicine (I took a look at one of these 3, and the residents kept falling all over themselves emphasizing how easy the place is--this kept me from applying).