I'm considering moving from San Diego to New York! Advice please!?

I am considering moving from San Diego to New York City in a few months. I am looking for a one bedroom apt, and rent budget at about $500-$1000 a month. I am interested in the East Village, Bronx, Harlem, Queens in no particular order. Is that wise to make such a move due to the winter coming? Also, what area has the best transportation lines? I have saved up $3,000 for living expenses to start. Is it enough? I've never been to NY, so any insight would be nice!