Is this lifestyle feasible in NYC?

I'm planning on moving to New York City by the end of the year (as soon as possible, idealistically), so right now I am in the planning stages. I have approximately $4,000 dollars saved up at the moment, which would go towards travel expenses (a train ride down from Boston so not wholly that expensive) and a down payment on an apartment. I do not have a job lined up for me, nor a place to stay. While I do not have a college degree, I have work experience. Honestly, I don't live a very expensive lifestyle - I don't drink or smoke, hardly buy clothes or anything. What part of town should I be looking in for apartments? Say I work two jobs - waitressing or something - will I be able to support myself? Thanks.