Chances at NYU Part-Time?

There are several questions in one here. Should you retake the GMAT? Sure -- you're currently somewhat below the median for this program (I don't think they post averages for the part-time program, but I'm speaking from experience), and you want to be maximally competitive. But another question that your post brings up is WHY part-time? Only because your GMAT is too low for Stern's full-time program? Or are there other reasons, such as employment? Also, are you seeking the MBA in order to switch your career, or will you stay in banking and use the MBA to jumpstart your managerial progression? Will you have an offer from your current employer for a higher role post-MBA?
You're younger than most part-time applicants I've seen, so the adcom will want to see a solid rationale for your decision. All these are questions you'll want to think through.
But to answer your most immediate question, yes, retake the GMAT. Based on my experience, you should be at a minimum of 680 to be truly competitive; 700 would obviously be even stronger. Don't stop working on this test until you have the score you believe is most representative of your abilities! Otherwise, you're selling yourself short.

Hope this helps,
Margaret Strother