I will be starting my anesthesia residency in July at Cornell. I interviewed at Cornell, Columbia, and Mount Sinai in NYC. I spent significant time at each -rotations and/or second looks. These were my impressions (keep in mind they are now twelve months old.)
Columbia - best reputation in NYC, long history of anesthesia, largest program in NYC, work somewhat harder than most. Most residents are happy with their education. Good autonomy. Washington Heights is not the best area of Manhattan (above Harlem) and facilities are a bit old, dark and grungy (may be going through renovations now.) Some residents live in the neighborhood, others in NJ and some even Downtown and commute by subway. Pretty much on your own to find living quarters.
Mount Sinai - residents extremely happy, friendly PD, decent area of Manhattan, near Central Park, relatively easier to be set up with housing. Has an anesthesia simulator. Excellent reputation and alumni contacts within NYC region but not a nationally recognized program. Hospital in bad financial shape (after miserable NYU merger attempt) and every department is struggling to find ways to save money.
Cornell - the "whole package" for me...great area of Manhattan, happy residents, good education, friendly PD, nationally recognized (Hospital for Special Surgery, Memorial Sloan, etc.), guaranteed housing, relatively good financial shape and beautiful facilities. Of note, Columbia and Cornell are now merged as 'The New York Presbyterian Hospital' which will only help the both of their hospital rankings and reputations.
I didn't interview at NYU because they were changing chairs at the time, though I hear it is a pretty good program now. St. Luke's is also a pretty good program and has a good local reputation. Don't know much about St. Vincent's. Long Island has an up and coming program at SUNY-Stony Brook with a nationally recognized chairman.
I pretty much interviewed at all the "top 10" programs in addition to the above. My philosophy was to go to a program where I would be happy, that would not close any options later in life, where I would get an excellent education, and where the residents/faculty consisted of people I would want to work with.