Hello sayantan1987, thanks for your question.
Your 680 is not a bad GMAT score, per se, but it would not move the needle as much as it would otherwise, given that you come from an overrepresented demographic in the MBA applicant pool.
My general philosophy is that your quants (e.g., test scores, GPA) open the door for you at programs, but your leadership experience and essays get you admitted. Moreover, you should select a program based on your career needs and culture.
As a first step, research schools where your 680 is close to the median or mean. You can be competitive here. For reach schools, if your 680 lies within the middle 80% range, you’d have a shot, but you’d need to lean on your essays to differentiate you and make your case.
Hope this helps.
Best of luck,
mbaMission Insiders Guides: http://www.mbamission.com/guides.php?category=insiders
Free Consultation: http://www.mbamission.com/consult.php