I would recommend that you check the Russian Flagship programs (http://flagship.americancouncils.org/russian/?q=content/domestic-flagship-programs) to see if any of them offer scholarships to students accepted in these programs. Of these schools, Wisconsin and UCLA also have strong physics depts.
If you’re interested in Russian Studies, the website, “Russia Direct” (http://www.russia-direct.org/) recently ranked Russian Studies programs. In rank order these programs were: Harvard, Wisconsin, Columbia, Illinois, Stanford, Michigan, Indiana, Berkeley, Georgetown, Washington, Yale, Ohio State, NYU, Miami (Ohio), Johns Hopkins, Chicago, Texas, Pitt, UNC, Brown, UVa, Arizona, Northwestern, Middlebury (Monterey), George Washington, Kansas, Duke, Penn State, Oregon, Florida State, Missouri, and Boston College. This ranking is for MA programs, but it gives you some idea of overall quality. You can download the full report by registering on the Russia Direct website. Of course, quite a few of these schools have strong physics programs, as well.