If you are OOS, gotta live off-campus to qualify for IS tuition, that's that.
IMO, dorms are definitely not "nice" by any stretch of the imagination but it is live able. All the utilities are folded into your rate (including laundry) which is nice, and is SUPER convenient for foundations years (classes are right across the street)
You're gonna have to deal with intermittent hot water and heat, and on occasions too much heat (the heat is still on in the dorms, its 71 and muggy outside), etc. Plus, the dorms are not that cheap (the major con for me, I currently live there, moving out for next year). They are in line with the going rates in the area, a bedroom in a 2bed apt will run you ~1100 a month, a studio ~1500, single room (think college dorm single, no kitchen, or personal bathroom)~750 (I dont remember the actual rates but its around there).
The surrounding area itself can be cheap and convenient, but gentrification is rapidly coming so there are tons of new luxury style buildings going up, driving up local costs. But that being said, new luxury buildings have their problems (often closet sized bedrooms and paper thin walls), but you will end up paying about the going rate of the dorms of a significantly nicer spot maybe 10min walk away, or even cheaper if you find something else prob in a un-renovated unit, or further walk. Use streeteasy, Nooklyn, the FB groups to find spots.
I'd recommend looking to see whats out there, then using the dorms as a fallback. Renting in NYC is an interesting experience, and if you've never lived in NYC before, apartment searching isn't very fun. Likely gonna need a guarantor, and be prepared to have to upfront nearly 3-4 months rent (first months rent (some places want two months upfront), security deposit, brokers fee (if you have to pay one)), and pull triggers fast as someone else is likely to swoop in if you are hesitant.