Most of the schools listed in post #13 do offer a lot of financial aid,; however, they represent a wide range of FA policies toward international students. Harvard, Princeton, and Yale are among the only colleges that for internationals are both need-blind in admissions and claim to meet 100% of demonstrated need. At the other extreme, UMichigan doesn’t offer any institutional financial aid at all to international students (according to its 2014-15 Common Data Set section H6.)
Also, many of the schools listed in post #13 do not offer communications majors.
At the undergraduate level, most of them focus on the liberal arts (either exclusively, or in combination with engineering and possibly a small number of other pre-professional majors). If you want a selective Chicago-area university where you can major in communications, consider Northwestern instead of UChicago.
https://www.communication.northwestern.edu/programs/major_communication_studies