I matched in 2011, and arguably EM has gotten more competitive even in just those two years. While your step I score is slight below average (mine was too) I think at this point in your medical school career, you still have the potential to become an "above average applicant." Step II, clinical grades and letters of recommendations will flush out and play a larger impact on your application then anything you've done thus far.
Here's your guide to matching into an EM program in NYC:
#1 Work hard in clinicals, especially your EM rotation, make sure you do your EM rotation in a place where you can get a SLOR, which is the academic stanardized letter of recommendation. You get it from places that have academic faculty that have residencies. Having 2 SLORs from two difference institutions will help.
#2 Don't hopefully do better on step II, DO BETTER ON STEP II. Okay fine, you got a below average score on step I, it's not a bad score though. You come back and do above average on step II, that looks good, residencies like that. Taking it in july vs. august doesn't matter, as long as you have your score EARLY in the application cycle to send to your programs to show your improvement and that you do a schedule that allows you to effectively study and prepare for step II.
#3 Do at least 1 "away rotation," and maybe even consider a 2nd one. I use quotes cause if your goal is to stay in NYC, then do the away rotations there, but at different programs then your own medical school. Work hard, stay late, be personable, read. Ask faculty you feel knows you if they feel they can write an excellent letter of rec for you. (a SLOR). Away rotations are audition rotations, programs that might pass over a slightly below average app, will highly consider you if they've worked with you and you've impressed them. I wouldn't pick "less competitive" places to do it, pick places you're interested in learning more about, where-ever they are.
#4 When the time comes, apply early and apply broadly. There are something like 15 programs within the five boroughs, all are competitive because people like NYC, but the truth is some are less competitive then others. I would consider also adding the two programs in Newark, NJ. You can live in Hoboken, still have a reasonable commute to work, and still have full access to NYC.
#5 Keep being a real person. Don't let medical school and medicine dominate your life, yes, it should be a big and important part, but when the time comes, your EM interview (once you get the interview) has much more to do with who you are and how you interact with everyone then the academic things you've achieved. So make sure you have something more to talk about then research.
The truth is you have like 20% of the information so far on judging your competitiveness. And while kudos for you for thinking ahead, you've got a while to go. Work hard, learn, take care of every patient like you would your own grandparent and try to have fun a long the way, you'll be fine, and you'll be able to match in EM, and probably have the options you want in NYC. Good luck.