A good starting point is to search for institutions that match your academic ability, by going down the U.S. News Universities and Colleges ranking, looking up each institution's 75th percentile SAT/ACT scores on the CollegeBoard website under the "Applying" tab, and comparing them to your own. An institution's "selectivity" is definitely an important factor. It is often recommended to apply to a good mix of "reach," "match," and "safety" schools.
For many, the next step would then be to gauge the extent each institution can assist international students financially. To this group, private liberal arts colleges would likely dominate the list of prospective colleges.
A university or college would also need to offer a good program in the major that the student is interested in. However, the definition of "good" vary. Some students may prefer their major to be a less popular one, where classes are small and intimate, and access to professors is ample. Others may want to have a lot of high-caliber classmates with the same interest, as well as leading researchers in the field to be their professors. Many schools offer selective special programs in certain disciplines. A lot of insider information on an institution's different academic programs could be looked up on the College Confidential forum.
Students interested in engineering or business would mostly look at research universities. There are also a few small colleges that offer excellent engineering programs. Many liberal arts colleges offer 5-year 3/2 dual-degree program in collaboration with research universities, but this path is much less popular. Law, medicine, dentistry and pharmacy are graduate programs in the United States.
International students might want to consider a school's location as well. If a college is in a metropolitan area, there are many things to do outside campus. The location also dictates the climate.
School "culture," i.e. conservative versus liberal, is a subjective factor that many look into. Insights can be gained by talking to current students as well as alumni.
Some colleges, e.g. Smith College, are single-sex schools.
Universities usually offer more academic programs than stand-alone colleges. Most stand-alone colleges are liberal arts colleges, which usually do not offer more vocational programs such as engineering or business. A few stand-alone colleges that focus on engineering and business exist, but lack the breadth of liberal arts disciplines. Universities, on the other hand, often boast a comprehensive range of majors, minors and electives, through its constituent colleges. Undergraduates at a university can normally register for classes across different colleges in the university.
A stand-alone college's focus is solely undergraduate education, while universities also focus on research. This generally means that students at stand-alone colleges have more interactions with professors, since professors have little research duty. While classes at stand-alone colleges are usually small and taught by professors exclusively, classes at a university are sometimes very big and taught by teaching assistants. Arguably, students at small colleges receive more personal attention than those at a big research university. However, students at a university might have more access to cutting-edge research. Still, it is often argued that small liberal arts colleges have a larger proportion of their student body that eventually earns doctorate degrees than large research universities.
Many research universities boast global prestige and academic reputation owing to research papers that they publish. Stand-alone colleges are less-known due to their relative research inactivity as well as smaller student population and alumni network.
Public universities typically have larger student populations. Private universities tend to have better student to faculty ratio.
They have lower tuition fees for students residing in the state that the university is situated. International students are charged out-of-state fees, which is higher than in-state fees but usually lower than a private university’s tuition fee. Private universities charge the same tuition fee to all students.
The student body at public universities consists primarily of in-state students. At private universities, the student population is diverse, coming from many different parts of the United States and overseas, with no group being the vast majority.
The admission process of public universities are largely merit-based, i.e. the most important factor is academic ability, even when the university is employing the holistic admission process. Private universities generally pay more attention to personal qualities when admitting students. In that sense, private universities are more “selective.”
Public universities do not offer any need-based financial assistance to international students, though they might offer a few merit scholarships. Many elite private universities extend need-based grants to internationals. Some others offer limited, but high-value, merit scholarships.
The following rankings, while serving as good reference, should not be used to conclusively judge the quality of undergraduate education of any institution, since each ranking puts a different weight on various aspects of a university or college.
U.S. News & World Report publishes an annual ranking of colleges and universities here. This ranking generally favors schools with larger endowments and higher freshmen's SAT/ACT score. However, its methodology may, and did, change from year to year.
Shanghai Jiao Tong University publishes the annual Academic Ranking of World Universities here (click here for the 2013 ranking of research universities in the United States). This ranking measures solely the research output of research universities, and does not attempt to rank the quality of undergraduate education in any way.
Times Higher Education publishes a reputation ranking of world universities (the 2014 ranking can be found here). As its name suggests, this ranking only measures how well-known a university is. Many outstanding universities in the United States are absent on this list.
Forbes publishes the America's Top Colleges list. This ranking puts a heavy weight on post-graduation salaries and student debts. Large research universities and small engineering and liberal arts colleges are stacked against each other on this list.
PayScale publishes an annual ranking of universities and colleges based on reported salaries. Figures are subject to numerous statistical biases. The 2014 ranking can be found here.