neurosci guy,
I'm also an outsider for these three schools (congrats by the way, that's amazing!), but I know some people who worked/went there. The general thought about the Rockefeller is that it is a GREAT place to do your postdoc at, since it is insanely biomed research oriented. As a consequence, as a grad student you have to be quite independent there because you probably wouldn't get as much guidance from your PI as you would in other places. I heard great things about Columbia, although I'm not sure about housing with them (Rockefeller gives a very nice subsidized housing). For such an elite school, Yale is considered very friendly and collaborative, so it is a good environment for a graduate student to thrive in.
there is a forum member here, don't remember the full nickname but it has "Alex" in it, I believe he also got in at all those schools (for microbio),maybe he can give you a good advice.