Your question is a very valid one and probably one that affects anyone living in NYC and starting at entry level in many different industries. First, know it's not impossible. If your heart is set on the publishing world, then you should pursue that route. I would start by checking both job search sites (Indeed.com, MediaBistro.com, etc) to get a feel for what offering and requirements may be, and pay offerings. Secondly, I'd check GlassDoor.com to get an idea of what entry level salaries may look like in NYC. Finally, consider where you'd want to live. Queens or New Jersey areas just outside the city are more affordable and only a hop, skip and jump away from the city by subway.
I lived in NYC for many years (lived in Queens, but worked in Manhattan) and started my career there as an entry level media research professional at an ad agency. Oddly enough, I ended up writing newsletters and it eventually led to other editorial/content management positions in other types of companies and industries. Publishing is an obvious route, but don't dismiss other potential avenues. Consider what is it about being an "editor at a publishing company" that you like? Is it the culture? Is it because there is an inner author in you and you are a lover of books? Or is it that you like to write/edit? If it's the third option, there are MANY ways to be an editor today. For instance, most websites hire content marketing firms to help populate blogs or social media presence (google a few content marketing agencies) to get a feel for what they might involve.
Good Luck , hope this was helpful! -Stefania