I'll assume you are talking about choosing a university for an undergraduate program, because making a choice for graduate school is infinitely more complex.
How do I evaluate the strength of my potential major(s) at a university?
How would I evaluate the social atmosphere without visiting?
How do I find out about the post-graduation outcomes of a particular university? (average starting salaries, unemployment rates of recent graduates, graduate school paths, etc)
To what extent will the location or prestige of a university affect my career options after graduation, both in the US and at home?
Should I be paying attention to housing options? (Would an international student struggle to secure a rent contract off campus?)
What other factors should I be paying attention to? (a couple of examples: free tutoring, whether the dorms close during breaks, whether there's funding for unpaid summer internships or research on and/or off campus, whether there are established study abroad programs and whether there's financial support available for a study abroad, how helpful the career development office is, whether this university enrolls enough international students to be knowledgable about international student issues)
And maybe most importantly:
Are admissions offices a reliable source of information? (In most cases not!)