NYU has a number of month-long electives; among them, most of the worthwhile ones are located at Bellevue. The places to see there are the CPEP and Forensics, which is the one I chose. It was a great month, with very fascinating and unique cases. Half of the patients came in from NYPD, the other half from Rikers Island. Teaching on the unit was superb and exposure to the residents was frequennt. I sat in on weekly didactics with the PGY2 class and was able to get a flavor for things. It was easy to arrange with NYU.
Cornell has a sub-I on the inpatient unit, 11N, which is essentially an audition elective. Visiting students get geriatric and adolescent patients, a good mix, and are supervised by attendings who also participate in the selection committee. You could do an elective at the Westchester site if your interest is in Geri or Peds; teaching there is dynamite, though you probably make fewer valuable connections in the long run.
I don't know about Columbia because my application never went through (they did cash my $100 check anyway, though... thanks guys). You will need a letter of recommendation just to get a foot in the door -- so start planning early. It probably is best to avoid child psych there, because you'd be at the new Children's Hospital, and away from the key attendings and residents who tend to concregate in Milstein or on Riverside Drive. Otherwise I don't think you could go wrong.
Whether you realize it or not, most visiting student electives are an audition of sorts. However, as long as you're a decent applicant all-around, a visiting student elective shouldn't make or break your chances of getting an interview at the institution of choice, or anywhere for that matter. Good luck next year!
