As someone who has research interests in the same field, I can tell you this: go with Chiba's advice and look for the professor, not the school. That being said, I'll normally always pitch for the University of Wisconsin; Jeremi Suri is one of the names in the Cold War field that you should be familiar with. But I know that he'll be on sabbatical this coming fall (he's got another book coming out), and they took a pretty good number of applicants last year in the 20th C. American/Cold War/International field, so UW may not be a good choice for this year.
Take a gander at Brandeis, Yale (if you like), WashU, and pretty much any other school that seems to gain consensus on this thread.
Good luck!