I was in NYC a few times while studying for the GMAT and I spent some time in the main branch of the public library (on 5th Ave). It was pretty quiet in there and I *think* they're open on Sudays (I don't remember for sure). I also spent some time studying in the library at Columbia (for inspiration-and with the hope that some of the "smart" floating around might rub off on me!).
Otherwise, I'm sure that no matter where you are, you could probably find a Starbucks or other coffeehouse to sit in for a few hours. I personally benefit from a little background noise (it makes my mind not wander so much), but most coffeehouses are pretty quiet, with other people reading or talking quietly. Actually, the best ones to study in are around colleges because there will be other people there studying.
Sorry I couldn't give more specific places, but I tend to wander around when I'm in the city.