I am not sure if this will help, because my background is a bit unconventional: Graduated recently from a European University with a combined BA-MA degree, major: Political Science, minor: Islamic Studies. GPA: not really convertible to US system, but not super good...
My biggest drawback is that it took me almost 10 years to finish what should be a 5-years degree - I have good excuses, but still... (2 years of exchange studies in China; spent 1 1/2 years doing internships in Switzerland, Syria, Kyrgyzstan and New York with various international organizations, and more than 1/2 year working almost full-time to be able to afford those unpaid internships; and in the final year I again worked almost full-time in Dubai and Kyrgyzstan). Dedicated a lot of time to learning the respective languages, so my language portfolio looks quite impressive (at least on paper ). GRE: 760Q, 730V, 5 AWA.
I basically applied to as many universities as possible, in the hope that someone might decide that my CV looks "interesting" instead of "unfocused and probably unable to finish a PhD in less than 10 years". Why NYU picked it up I really don't know - I was under the impression that they are heavy on the quantitative side, and nothing in my application points to such a focus: my writing sample was purely qualitative, and I attended only 3-4 statistic-related classes (admittedly with quite good marks). Mentioned in my sop that I would like to do apply network analysis to authoritarian regimes and therefore would like to work with Adam Przeworski, Bruce Bueno de Mesquita and Alastair Smith (and mentioned some of their papers related to authoritarianism).
Hope that helps - as for me, I am still a bit confused about NYU's choice, but far be it from me to complain...