New York University
New York University is a school of 'high'er education located in Greenwich Village. You will make tasteless jokes about NYU students for about a semester before you realize it makes you look insecure. Then you will try to join their fun scene downtown, to no avail.
Campus design: fail
What's not so well known about NYU today is that they used to have their own McKim, Mead, and White designed campus, built around a domed library, which they then had to sell off to pay the bills: the University Heights (Bronx) campus, which was built around the same time as Columbia's move to Morningside Heights.
And here's the real difference between NYU and Columbia: NYU nearly went bankrupt in 1973 and sold off its campus to New York City. So NYU slunk back to its then-decrepit Washington Square Park, Bronx Community College is now located in a gorgeous MMW-designed campus, and we're still sitting pretty on our pretty campus. Take that!
Library quirks
What also might not be so obvious is the fact that all Columbia students with a valid CUID have access privileges to NYU's Elmer Holmes Bobst Library on Washington Square South through a reciprocal agreement between the two schools.
I suppose posting this may result in an influx of pseudo-hipsters at Butler, but then remember that NYU kids don't study (or read). This means that Bobst Library is almost always empty, except for the homeless. Just keep your head up for the divers when in the atrium.