what are my chances with a relatively low gmat score

IMO you should think about retaking the GMAT... just think of your competition. I think you do fall in the 20-80% range, but if that was your first time taking the GMAT and you scored a 680, you will probably score higher with some more studying.

Your GMAT score is only one of many components that schools will use to evaluate your candidacy. A 680 will not necessarily keep you out of a top school. How are your undergraduate grades and your MS grades? (and where did you get your MS?).

Will you have fabulous recommendations? Is there anything particularly unique about your background? Do you have strong extracurricular activities and volunteer work?

For top schools, you will need to be strong in many (if not all) areas. Standford will be very challenging for your profile (based on the limited information I have). Berkeley, UCLA & Duke might be good targets if all of your other elements are very strong. Yale is the least competitive of the schools you listed so you probably have the best shot there.

If you are worried about the other parts of your application, I might try to retake the GMAT so that you have a bit more clarity. You have plenty of time, and, at worst, you'll still have your 680.