Do it. You will love it.
I spent $900 to share a nice, quiet 3 br condo with 2 other gay guys in the Elmhurst section of Queens. Its only a 20 minute subway ride into Manhattan. I had the place from April '08 to August '09, but only lived there for maybe 6-7 months total. I loved it there. I REALLY loved it there. Every day, I said to myself that I should have moved to NYC the day I turned 18. However, I've got to be in Florida now, and love Fort Lauderdale too.
Queens is like a slow paced small town, but with tons of people. Manhattan has got so much energy to it. The people are friendly and have plans for their lives. I felt safe every place I walked...and I walked all over Manhattan. Brooklyn is another great area to live. Younger people tend to live in the boroughs, as its lower cost and the subway system is excellent. Check out the apartment share and temp rentals on craigslist.org.
Now is a good time to go. You can get an x-mas job in retail noooo problem. NYC is a shoppers paradise. Have sleeping accommodations lined up for your first few nights...a sublet or hotel. These things buy you time to find semi-permanent work and living space.
For money, $4,000-$5,000 should easily do it...you often need first/last/security for your apartment ($2,500), say about $1500 for other living expenses....including a scarf, wool hat, gloves and boots...lol. If you need a bed, get an air mattress and put blankets over it.