The closest airport to Columbia is LaGuardia Airport (LGA). The M60 SBS bus from LGA airport is the most inexpensive transportation option to/from Pupin Hall (hop on/off at 120th Street and Broadway stop). Before boarding, you must pay the fare at the collection machine at the bus stop, and keep the receipt during your trip. Taxi rides to/from LGA can take anywhere from 25 minutes (no traffic) to more than an hour (rush hour traffic), and on average about 45 minutes.
If arriving at JFK International Airport, taxi rides can take anywhere from 45 minutes to almost 2 hours, depending on traffic conditions. There is also an AirTrain+Subway transportation option between JFK and Columbia campus (see, e.g., google maps for available routes and travel times).