This is another matter in which international students really get the short end of the stick, because at this point I think visiting the university is invaluable and the trip for internationals is too expensive for the university to fully cover (though most will reimburse you the $500 or so that they reimburse domestic applicants). As an example, I was choosing between Berkeley and Cornell for CME, and there was a very well-known professor at each that I was interested in working with. Upon visiting, it was immediately clear to me who I would rather work for and that ended up being a very large factor in my decision. For domestic applicants, you really have to visit, talk to the graduate students of the people you are interested in working with and talk with the professors as well. Ask lots of questions, and you will get a really good impression of which environment you would prefer. If visiting is not an option, I would recommend calling or emailing professors you are interested in working with, and get in touch with their graduate students as well. The good news is, although the decision feels excruciating, you can't really go wrong at this point so count your blessings!