What's the best place to live on a low budget given a life-consuming job in Manhattan near Madison Square Park? And how low can I go both before and after unintelligible-but-critically-important-tax-stuff?

Here's a counterpoint: with a $2000 take-home and a roommate, I lived on $1000 and put another $1000 in the bank. (So then I used the money in the bank after I made various mistakes, but it sure was nice to say F you, I have $10,000 just sitting around.)

NYC is all about subway lines, and Madison Square Park is, as http://www.metafilter.com/user/132207 points out, very handy to the nearer parts of Queens (F, M, N and R lines). A studio to yourself with a half-hourish commute is going to run around $1200; with a 45 minute commute you could probably find something for $1000 or even a bit less depending on your tolerance for sketchiness. Either way that is a lot to be paying in rent out of the hypothetical $1800 take-home mentioned above, so you might want to think about, for now anyway, a share, which still is likely to be in Queens or the nearer parts of Brooklyn. I am not a huge fan of Upper Manhattan, because it's a long haul from 201st Street down to Madison Square. On the other hand the apartments up there are mostly pretty big and there are a lot of owners and renters looking for someone to share. Assuming you get decent medical insurance through your employer, this is do-able for $40K. Below $30K you may need savings or help from parents to get by for a while.

(1) how much money I'll actually get per month?, and (2) how much the job offer salary would need to be in order to result in that monthly paycheck? When I made 40k, my take-home, after taxes and health and 401(k) contributions, was a bit under $2300/month. Revise downward from there. My second question is then, where and how are the best places to look for housing given this circumstance? Where in terms of areas of NY, and how in terms of good sites to use to track down specific housing opportunities. Astoria/Sunnyside/Woodside/Jackson Heights in Queens would probably work well for you. Crown Heights or Ditmas Park in Brooklyn, or Harlem in Manhattan. At 40k, you could get your own place for $1000-$1200 (if you don't wind up with a landlord who is a stickler for the 40x income requirement), but money would be real tight and you'd probably be looking at a long commute. You could also get a share for $700-$900, have more disposable income, and probably a shorter commute. At 30k, or even 35k, the your own place option is essentially out. A Craigslist roommate situation might also allow you to sublet and sort of feel out where you'd like to be without having to sign a lease. This is excellent advice.

Finding a roommate you (sort of) know: network network network. A lot of people I know post roommate openings on Facebook and send out emails to everyone they know before going the Craigslist route. Tell everyone you're looking. Shorter commute: follow the subway. Astoria or Lefferts Gardens (bonus: near a big park) might work for you. Or, if you lived in Harlem, you could bike through Central Park to work and have a pleasant and decently short commute. (Sans sunflowers.) Don't choose a neighborhood until you have a chance to explore a little. Try getting a short-term sublet first, then look for a longer-term situation. People have roommate interviews around here, so no one goes blindly into a living situation. You will find people your age, unless you are, like, 65. (I'm guessing not.) You will not be able to live alone, full stop.

I think Hudson Heights, in the Washington Heights neighborhood, might be okay for you. It's in Manahttan, but it's less expensive. I think it looks pretty, but I'm a weirdo, and I'm comfortable with lots of Spanish speaking folks in my world. YMMV. I love the pre-war buildings (they remind me of Squirrel Hill in Pittsburgh where my Grandparents lived.) This part of Washington Heights looks very suburban and quiet. I saw a few http://streeteasy.com/nyc/rentals/hudson-heights-manhattan?page=6&sort_by=price_desc. Which is do-able if your dream job offers $40,000. (Less so on $30,000) This was an incredibly cursory look, you might find less expensive places with a deeper-dive. Just a thought. If you got to NYC, take the subway and walk around to see if you vibe on it.

I'm a bit spoiled when it comes to roommates, I've been sharing an apartment with 2 great friends for the past 2 years. I've also been scarred by a stint with 2 roommates who were pretty hellish to deal with (never around to the extent that collecting rent became a very stressful ordeal.) I like living with other people, but I'd want them to be roughly my age; and the idea of moving in with someone without knowing them first kind is almost unacceptable. If there's a way around that concern though, I'd be all ears. You can't afford to live alone, so you have to get over this. Sorry. I've had some good roommate experiences on Craigslist, and I've had some bad ones, but unless you know someone in New York who can help you find a roommate, you really have no choice. A Craigslist roommate situation might also allow you to sublet and sort of feel out where you'd like to be without having to sign a lease.

http://www.triptropnyc.com/?f=madison+square+park&t=&z=12&lat=40.741794637954946&lng=-73.95721435546875 is a visualization courtesy of TripTrop showing which neighborhoods are 30 minutes from Madison Square Park. Might be helpful to cross-reference with, e.g., http://www.padmapper.com.

Yes, you will absolutely need to do a roommate situation if you are going to afford to live a remotely enjoyable life. At 40k, you could maybe maybe get a place of your own, but it would have to be $1000 a month which is incredibly hard to do even way out (but not impossible--I'm one of the lucky ones, but it took lots of maneuvering and right place/right time stuff), and you still wouldn't have much left over. So I would find a roommate situation. Start with finding a sublet, maybe for a month or two or three. Craigslist is really only the place to go unless you can send out a facebook or email blast to everyone you know who might know someone in NYC who needs a roommate. With a sublet, you can get a feel for your commute, neighborhoods, cost of living, etc. and figure out what you'll really need/want. You can find rooms that are in safe not-too-far-out neighborhoods for $800 a month easy. $900 easier. Again $500, $600, $700 are harder, but not impossible (again, I've done it, but again, I've been lucky). But you can do it on $30k, though you'll have to be very frugal. What you want in a neighborhood will determine which neighborhoods you look at. Speaking only for Brooklyn, the closest neighborhoods in which you will have the easiest time finding an affordable room are Bushwick, Bed-Stuy, Crown Heights, Ditmas Park, and anything east and south of those (but east and south get to be a long commute, or in some places, not very safe). So start on Craigslist. Just know that when you find a place you like and you think you have a good vibe with the roommate(s) you need to offer them money pretty much right then and there to secure it, because they will have tons and tons of people interested. You need to be prepared to pay first month plus deposit upfront. Possibly even first month, deposit and last month (i.e. 3x month's rent). So make sure you come to town with a good bit of money in the bank. You need to learn to trust your instincts in this regard, because you won't be allowed much time to deliberate. On that note, if you'll be here this summer, I might know of a room in a really nice place, in a nice neighborhood with roommates late twenties/early thirties that would be a 30 minute commute for $700-$800. So memail me if you're interested. Must love cats :) Do keep in mind though, that if this is a standard 9-5, you can always try to supplement your income with extra work at night or on the weekends or freelancing or ebaying stuff. Bottom line, if you're scrappy and don't have high standards, then you can make it work. But under 30k will definitely be pushing it. Good luck!

At that salary point, you're going to need a roommate, or live pretty far away.