Unfortunately, Stony Brook is rather expensive for a place that isn't in or even that near a city. There are few apartment complexes, so most of the off campus housing is in shared houses or else apartments that people have carved out of their basements/garages. Shared rent can be reasonable (in the 500-700 range), but getting your own place is quite difficult (unless you want to pay 1000 a month for a basement with a hot plate and a microwave).
As for the town itself, Stony Brook is a small village surrounded by pretty bland suburbs. You could consider living in Port Jefferson though, which is a nice little town nearby. The train to New York takes over 1 and a half hours from Stony Brook station, but only an hour from Ronkonkoma, which you might end up living closer to anyway. You absolutely will need a car.
There is some on campus grad housing, but I think single students have to share rooms, so you could definitely do better off campus.
On the plus side, SBU has an incredibly diverse student population, with students from all over the world. Going in to New York for the day is easy, though I agree that if you needed to be there every day for some reason, you would quickly wear yourself out commuting.