If one is not fortunate enough to bring a car to school, or make friends with someone who doesn't mind driving, public transportation will become your livelihood. Stony Brook University's campus is fairly well removed from places like grocery stores, movie theatres, and other amenities. The HART and Suffolk County bus systems are pretty cheap, but don't run all that often to the places you may need to go. Keeping tabs on their schedules can be important.
The Long Island Railroad is your key to getting out of Stony Brook all together. It is much cheaper to take a train to the city, and much more convenient than other modes of transportation. It is very reliable, and not all that expensive. A train to Penn Station, in the heart of the city, runs about $7.25, and the subways from Penn go to any point in the city one desires to go. The ferries offer an alternative to driving all the way around the city, or even through it. A ride across Long Island Sound takes about an hour and a half. There are concession stands on the ferries and outside decks. They are definitely a quicker way to travel up to New England, and more fun. Long Island's MacArthur Airport was renovated, with an expansion letting in many more airlines, and making many more flights available. The postmodernist look is both cleaner and more spacious.