Few if any students bring cars to Columbia. Apart from the fact that driving in New York City is essentially a game of Russian roulette, having a car in the city is expensive and inconvenient. Parking is virtually nonexistent at Columbia, apart from a few nearby garages and any side street spots you can manage to find. That is to say, there are no Columbia-owned parking lots for students.
Luckily, New York offers lots of transportation options to make up for the sacrifice of driving. The subway is a convenient and relatively cheap option, and can take you just about anywhere you need to go in the city. If you are in more of a hurry, you can take a cab (though, be warned that most cab drivers don't want to take you to Brooklyn or the airport). If you are in no hurry at all, you can take a bus, ride a bike, or walk anywhere you need to go.