I'm working on a lesson about interviews for Admissions Starter. Yes, interviews can be significant, but many schools don't use them. Prominent schools that invite some candidates to interview include Harvard and Chicago.
I've heard many good things about Georgetown and NYU in terms of int'l law. I'd check those out :) FYI: NYU is ranked higher than Georgetown if my memory serves me correct.
... very interesting to read on NYU, which is an example of ... a disadvantage. http://www.law.nyu.edu/jdadmissions/applicants/admissionsinformationandinstructions