There is really nowhere to park on campus or around campus. If you do drive to Barnard, make sure that you have plenty of time to get where you're going because it is not uncommon for a parking spot search to take more than half an hour. The school does not issue parking permits, nor does it have a place for anyone to park except instructors and administrators. This isn't because Barnard doesn't care about how students get to school, but because no one, except people who commute from upstate New York or New Jersey, drives in New York City. It's just much easier to walk or to take some form of public transportation, unless money is not an issue at all.
While Barnard's parking scene is almost laughable, a person has to take into consideration that most students live on campus, and, of those that live off campus, most live in Manhattan, and they most likely do not need to drive to campus, either. New York City's public transportation system is very easy and cheap to use, and that is how most New Yorkers get around in this pedestrian-friendly city. This may be strange to people from the South or the West Coast, where driving is a must for nearly everyone, but, in New York, driving is a luxury and not a necessity. Barnard really cannot help the street parking situation around campus because that is run by the city, and to somehow allot for on-campus parking for students would just be unnecessary.