Hi Radhika - first of all, congrats on bumping up your GMAT score from the original level (we saw that you originally had a 580 or so). Unfortunately the current 630 is still very low when we're talking about the best bschools, and so we
generally agree with some advice you've gotten from some of the other consultants whom you've asked for input from - but there's some details here that we need to call out, that could change the picture.
Before we do that: We need to say that yes, a higher GMAT would help A LOT, so if you are confident you can raise the score further, then definitely retest.
A main reason for that advice is not only because the GMAT is low, but also because you said that your GPA is "3" - if you mean "3.0 on the U.S. 4.0 scale" then this is another weakness, and that would be two strikes against you. A higher GMAT cannot completely offset a low GPA but it can certainly help.
Now, the reasons why the current GMAT
might be enough (we have "might" in italics for a reason!! these factors add slim possibilities, they do not say that the current GMAT is good enough):
1. Your strength is on the quant side. This is more important than verbal - not that verbal is irrelevant, but the quant is quite good. It's easier for the adcoms to go along with this score breakdown than if it were flipped.
2. You're trying for NYU part-time. The part-time programs are always less competitive. NYU P/T is still very competitive compared to many other good business schools, but it's definitely easier to get in than their full-time track. Your essays would need to be AMAZING and you'd need to show very strong reasons why the MBA is the right next step for you, with great evidence of leadership and impact in your past - but it's on the edge of possible to get into Langone with this GMAT score.
3. You're a woman (correct? if not, then big apologies!!

) The schools will not compromise on standards for women, but they are all trying to increase their ratios of female students. This is a slight advantage. They won't overlook big weaknesses - they need to see that you can handle the difficult curriculum - but there's fewer apps received from women and therefore it's somewhat less competitive. (Somewhat. Marginally. A bit.)
Hopefully this helps you decide your next steps. If we can answer other questions please don't hesitate to ask!
EssaySnark