While I agree that NYC is most likely the most impressive city (in the country or even the world, perhaps), I would undoubtedly go to Boston U. Here are my reasons:
1. NYU puts first-years in DORMS. A rusty sink in one corner and a coed bathroom shared by everyone on any given floor. Not blaming them, since it IS New York and great housing would be impractical from a financial standpoint. Still wouldn't want to live there, though, regardless of the reason for it.
2. BU is more about academic medicine (as already mentioned, and as is generally true about all of Boston). If you're little interested in research or academia in general, NYU gives you outstanding clinical experience at Bellevue. But the clinical experience is still great at BU, and you get new and impressive research facilities and funding.
3. New York City, despite its splendor, is a bit dirty, crowded, and hectic. Boston is historic and beautiful, and BU is in a particularly great area (right next to the South end).
4. Perhaps least important is ranking. US News puts BU slightly higher than NYU, and looking at matters like research funding and new facilities (over the past 5 years or so) really makes clear a sort of upward trend for BU (whereas NYU seems kind of static, albeit a great school).
OK, just my two cents. In case it isn't obvious, I've been accepted to BU and am giving you the reasons why I'm definitely going to attend. Sorry, don't know much about Tufts...