Richard Florida does a quick and dirty meta-ranking, pulling from a variety of global cities indexes.
What Is the World's Most Economically Powerful City? - Richard Florida - Business - The Atlantic
New York is # 1, but 4 other U.S. cities make the top 20: Chicago, Los Angeles, Boston, Washington, in that order. I don't put a lot of stock in this kind of thing as far as absolute order, but these lists do usually hit the main points of what differentiates the more important cities from the ones that don't make the list.