1. I moved this to the pre-PT forum.
2. NYU is done through PTCAS, so they'll theoretically see your scores on that application since PTCAS sends it out. I wouldn't send a score report though. First off, it'll cost you an extra $20 or whatever it does to send scores, and I'd rather use that money to buy food
Does NYU say it's optional or do they imply that GRE won't make a difference (some schools say they won't even look at the GRE)? Does it give any average score for applicants/entering students on the NYU info page? If it looks like NYU doesn't look at scores at all, don't waste your money sending scores. Not to sound discouraging, but while you have legit, solid scores, they seem to be just around what most other strong applicants have from what I've seen (give or take a few points), so if you're thinking it might edge you in one direction, it might not actually do that (if you had gotten a 650+ in verbal, well over 700 in quantitative, and at least a 5 in writing, then maybe).
You seem like you might be a well-rounded applicant though with those scores, so let your applicant speak for itself. Make sure other areas are strong enough that your GRE won't be the best part of your app.
Hope that helps? This is just my opinion, of course. Take it as you will