Reply #18: A couple more suggestions

[KurtNYC]

Get an unlimited MetroCard ($7/day) for at least one of the days you will be here. You can hop on and off of subways and buses all day long. Saves your legs and you won't have to worry about paying again if you get on the wrong train or miss your stop, etc.

On October 9th, if you have any inclination whatsoever, join us at Strawberry Fields for an all-day and most of the night sing-along tribute to John Lennon. It's his birthday! Take the 1/2/3 to 72nd or the B or C to 72nd and walk about 50 yards into Central Park -- you will find 100+ people at the Imagine Circle singing our little Beatle-lovin' lungs out. There will be musicians also -- guitars, electric bass, drums and sometimes a guy with sound effects (for "Yellow Submarine", "Day in the Life" etc).

If you are a Food Network fan or just a foodie, check out Chelsea Market(A/C/E train to 14th then walk one block over to 9th Ave). This neighborhood is also heavily featured is "Sex and the City":
http://www.chelseamarket.com/enter/themarket.html

On Saturday or Sunday, go to Washington Square Park which is always buzzing with activity and bands then stop in for gelato, pasta or a glass of wine at Mario Batali's gourmet-on-the-cheap Otto (in the 1 Fifth Avenue building, just north of the park):
http://www.ottopizzeria.com/menu.html

If you go to the Met Museum (great collection of Impressionist artist on the middle of the 2nd floor), either pick up a button off the ground, ask someone departing for theirs or simply go to the admission booths and tell them you are a student and only want to pay $5. Admission is technically free but they suggest a whopping $20 these days. You can pay whatever you like (including Zero).

The lower end of Central Park is especially neat. You can peek at the sea lions of the zoo free then walk down the swanky part of Fifth Avenue (59th to 42nd). You will see the Plaza Hotel (featured in the opening of "Friends"), Tiffany's (they don't serve breakfast btw ;-) ), St Patrick's, Rockefeller Center, and the Public Library (take your picture with the lions).

As for Columbia...
Check out this outrageous list of people who have graduated from Columbia University (and their descriptions are on target too; see Dick Morris for example).
http://www.nndb.com/edu/477/000068273/