I find your dilemma to be a very good one. They are all top MA's, definetaly among the most reputable, but NYU would most probably be the best choice,though I have heard special emphasis is laid on mathematics (but still that's perfect for modern economics). On the contrary, Duke is well-reputed concerning its emphasis in Financial Economics. However I think that LSE's Msc in Financial Economics might have been a great route towards a phd in Finance.
Anyway, I find myself in a respective dilemma, but since I got rejected from NYU choosing between Duke and LSE MA in Econ is simply impossible for me. I want to do monetary economics in the future, and I feel that Duke university lacks LSE's world-class reputation, but Duke will also give me more chances in getting into a top10 phd in econ afterwards.
If your dilemma has been answered, please help me resolve mine as well! I have posted a new topic for me too.