I've visited NYC a few times. I'm not rich, so I've always stayed in hostels.Much, much cheaper! Not only that, you can actually meet people, which has never happened to me in a hotel.
If you don't want to sleep in a dorm, you can pay extra for a single room. Pure guess-3x more.
November or January, there won't be many travellers, so even if you're in a dorm there'll be few other people there.
Couple of years ago stayed in Chelsea hostel ( I think)- Manhattan-$30ish in January.
Stayed in a hostel in Borough Park, Brooklyn which was OK and cheaper, but it might not be open those months.
Wherever you go, make sure it's CLOSE to the subway and buy a 7 day pass for it.( last time I went $31).
Sorry, I haven't answered your question re:hotels. Too expensive.