Thoughts about housing from a native New Yorker:
Yes, it's very very expensive. It only gets cheaper if you live:
1) in an undesirable neighborhood
2) far from the subway
3) with a LOT of other people
But here's a little good news...
The Upper East Side (where I've lived for about 4 years now) is clean, safe, on the 6 train, and relatively inexpensive. I live about a 5 minute walk from the 77th St Station in a one bedroom and pay $1650. It's a 2nd floor walkup.
In general high floors in walkups can be pretty reasonable. Also, the Upper East Side is improving overall so you can go up to about 102nd St before it starts to be a bad neighborhood (even further if you're on Lex/Park/Madison etc).
If you don't mind a further walk to the subway (or a bus commute) the apartments on East End/York can be cheap too.
Anyway, I've lived in Chelsea and the East Village and while they're certainly cool places to be the Upper East Side is on it's way up in fun-ness and much, much, cheaper.
Also, don't immediately go to a broker. That's expensive too. If you do, negotiate the fee. And probably don't use Craig's List unless you are seeking to live in someone else's apt. Walk around neighborhood and look for signs on apts. Or "No-fee" buildings. They don't advertise because they don't have to. Put a little foot action into it.
If you just want a room then put a post up on Craig's list in the "seeking" area. People don't post the amazing room they have available because they'll get flooded with responses. They scour the "seeking" posts to find normal people. (Graduate students tend to be a prime find).
Just my 2 cents.