Depending on where you work in Manhattan, that would put you either in various locations in Brooklyn (Financial District and anywhere up town), Riverdale in the Bronx (Mid-town West), Queens in places such as Astoria, Forest Hills, Sunnyside (Midtown down to the Financial District), and if you want to take the LIRR you can go out to the border of QUeens/Long Island (Bayside, Little Neck etc) where it is a lot more suburban. Also, if you don't mind filing two state taxes, you could consider NJ on the Path. As you can see, where you work and the ease of getting there by public transport is critical...you are going to need to ride the trains to figure out the best places to consider. And just as a note, we aren't allowed to discuss crime statistics in the various neighborhoods, but there are a few sites that will provide maps and statistics for you.
Bond New York
Manhattan, Brooklyn, Queens
For the best options aside from Manhattan, see the link below from a blog post I wrote a while back about this very topic. The comments about having a job and/or guarantor are spot on, though some smaller landlords in the boroughs will allow for you to pay rent up front in lieu of proper financial qualification with documentation.
If that doesn't work for you, it sounds as if the other advice here is pretty good.
Also be aware that New York is probably the safest large city in the states. Since you have flexibility of location and would be willing to commute, check into Queens. It's much more affordable and as I live in Queens, I can tell you there is reasonable opportunity here. Good luck.
A job is a MUST HAVE requirement - without a job you need a guarantor - someone willing to sign a lease for you/with you and who earns enough money to qualify as your guarantor.
You need to have at least 2 months of rent and in most cases a real estate brokers fee equal to one month rent up to 15% fee. Manhattan is very expensive start to look in Queens or Brooklyn. Go to the website and search for a studio apartment that is one room, a kitchen, a bathroom. The other suggestion I have if looking for a roommate situation. If you get a job, you can ask people at work to help you.
I recommend if you can, come in for 3 months to find a job first.
Licensed Real Estate Professional
25 Hudson Street
New York, NY 10013