This page is intended to help you figure out how to get around NYC once you get here.
In most of NYC, walking is the best way to get around short distances!
Taxis are plentiful (12,000!). It costs $2.50 on entry, and $0.30 per unit (where a unit is either 1/5 of a mile, or 90 seconds of waiting time)
The subway is the most efficient for of transportation in NYC, and the Metrocard is the most convenient form of payment (as well as allowing you to transfer from bus to subway). The bus is more scenic, but slower. There are online maps of the routes.
The Columbia University subway stop is at 116th St and Broadway (and shown as the 116th St stop) and is serviced by the number 1 and the number 9 subway trains. Don't get on just any subway to "116th St" because you may end up in the wrong part of town! The buses that serve the Columbia area are the M11 (on Amsterdam Ave), the M4 and the M104 (on Broadway). Buses generally stop every two blocks or so.
Here is some info on the Metrocard, and what it looks like:
If you have some free time in the city, feel free to explore - it is the best way to get to know the city!