Apartment information (PM me for anything you'd like to add):
Upper West Side:
15-30 minutes to school (all distances are by train unless walking is faster and ranges are based on closest part of neighborhood to furthest part).
Good: quiet, super safe, decent subway access to the whole city except Queens and the UES, prices are among the lowest of neighborhoods within 1/2 hour of school, Central Park access, better restaurant options than UES, all around good neighborhood for people not wanting to go full-NY.
Bad: Not a young crowd, a little out of the way, restaurants are a little expensive and geared toward 30-somethings.
Upper East Side:
20-40 minutes from school.
Generally similar to the UWS. Slightly cheaper - especially the further east you get. Restaurants are a little more expensive and as there's only one subway, access is pretty bad.
10-20 minutes from school.
Pretty expensive (except maybe Hell's Kitchen). Access to everywhere in Manhattan. Tons of restaurants and bars - pretty expensive. Incredibly packed so not great if you're from a small town and don't want to be completely overwhelmed.
Not really a place where students live except Hell's Kitchen.
East Village including Stuy-town:
10-20 minutes (generally walking only since there's not really a subway over there). Get a bike!!!!
Awesome restaurants and bars at great prices. No subway access without walking over to Astor Place or Union Square.
I didn't really look at prices there but they're generally high and the housing stock is not very good.
West Village/Greenwich Village:
Really expensive unless you're in student housing (which is still pretty high. Great bars and restaurants and obviously incredible proximity to school.
Brooklyn part 1 (Williamsburg, DUMBO, BK Heights, Fort Green, Boerum Hill, Park Slope etc.):
20-40 minutes generally. Pretty bad late at night.
Prices are similar to UES/UWS in many areas with slightly worse train access. More college-y and a greater number of students there than uptown. Great bars and restaurants at awesome prices. However, if you're a BK person, you probably won't hang out in the city quite as much and it can be a little tough to get people to come out that way.
Brooklyn part 2 (Prospect Heights and other outer neighborhoods).
Cheap and really inaccessible. Be careful - some of the neighborhoods are still a little unsafe.
Queens part 1 (Astoria and Long Island City)
25-40 minutes to school.
I'm not too familiar with the area but I do know that some places in Astoria are incredible for the money. The neighborhoods in Queens that are close to MH are very safe.
Queens part 2 (further reaches)
far and not necessarily a great place to be at night. Super cheap and inaccessible. Some of the neighborhoods (i.e. Forest Park) are supposed to be pretty nice but I don't really know much.
Streeteasy.com - you can sort by price, whether or not you want a broker, bedrooms, etc. Make sure you are looking at rentals rather than sales.
Padmapper - pretty good but NYC apartments move quickly and a lot of these will be unavailable when you call.
NYU law coases listserv and NYU listserv - the general list-serv has an apartment search function and if you ask for help on the law-specific listserv, people are pretty helpful.
Insurent.com - for people unable to get a guarantor, a limited number of landlords will take insurent. This is a program where you pay a percentage (generally between 75 and 100% of one month's rent for this company to provide a lease guarantee, which is a type of insurance that they pay your landlord in the case that you default on your lease. They still generally require good credit, or a parent guarantor that makes 50x your monthly rent, but it's a lot better than 80x. Obviously, there's the same problem of essentially throwing money away as there is for getting a broker.
Should I use a broker?
Not if you can avoid it. Brokers in New York charge between 8% of your annual rent and 2 full months of rent. They do provide a valuable service - there are amazing, well-priced apartments that cannot be gotten without their exclusive access. They can definitely help if you're unfamiliar with New York and don't want to get screwed on your cost/value. However, note that a 2K per month place without a broker ends up costing 24K for the year, and you can only get between $1725 and $1850 worth of apartment for the same money if you use a broker.
How much money do I need to move in?
That really depends. If you have all your ducks in a row - a NY/Conn/NJ guarantor who makes 80x your monthly rent, you can pay first month's rent and a security deposit (generally one month of rent). Sometimes, they require first, last, and a security deposit. Don't forget that even if you're not moving particularly far, and aren't using a service, moving can be a bit expensive.
If you don't have a guarantor, things can get really tricky. We ended up paying first two months, last two months and security (five months rent). If you definitely can't get a guarantor, be prepared to pay up to six months rent. You really should try to live on campus if you're in this situation.
REMEMBER: loans are disbursed around the time classes start. Unless you can find a short term sublet, you won't be able to use loan money toward these costs.
In NYC, demand for apartments is way higher than supply. Therefore, landlords will do everything they are allowed to legally do to guarantee that they make money, and can create horrible hoops to jump through. Generally, this means that you must make 40x the monthly rent. So if you have a 2k/month place, you need an annual salary of 80K. Unless you have a roommate that makes bank, you can't fulfill this requirement. Therefore, you will need a person to guaranty your lease who makes 80x the rent. This can sometimes be a combination of people (i.e. your parent makes 90K and your roommate's parent makes 70K). However, many old-school landlords will not take guarantors from states other than Connecticut, New Jersey, or NY. See the section on insurent for possibly getting around this.