I've written for tv, animation, film, comics, and videogames. I did that by being in L.A. to break in.
BUT you should take advantage of being in NYC to pursue any and all opportunities that might come along. The other commenter had good suggestions.
NYC has always been more expensive than L.A. The one advantage to NYC is mass transport, so that you don't need to have a car. Whereas in L.A., you MUST have a car. It isn't a luxury; it's a necessity. Be warned, the traffic is a nightmare, but it's a fact of life.
Most staff jobs for TV shows are in L.A. If your goal is to work on TV series, L.A. is your best bet to break into that. Make all the connections you can. Network like crazy, because you'll have a very hard time getting your foot in the door without personal connections.
Christy recommends the following next steps:
- Contact the east coast branch of the WGA, WGAeast, and see whether they have mentoring programs or anything else that might be useful to you.
- Write many scripts of different lengths and types. You'll need strong spec scripts to show what you can do.