in terms of the schools, make sure you actually spend time looking at classrooms, study areas, dorms/apartments, and libraries, since you'll spend lots of time in them and they could affect your experience a lot. also try to get a sense for the neighborhoods around the schools, since they're significantly different.
new york is great. depending on your interests, museums like the Met and MoMA can be great - check online to see if they have special exhibitions. soho shopping is always fun, though there are mobs of tourists.