A couple of things you might consider as you think about US colleges/universities:
There are something like 3000 US universities, and they are quite varied. Among excellent ones, some are right in major cities (like NYU), some are practically in cornfields (Grinnell). Some LACs and others have approximately 2000 students; some state flagship public universities (Michigan, Texas) have more than 40,000 undergrads and many more grad students. Many are in “college towns” where the school is often the biggest economic engine in town. Generally speaking, LACs will provide smaller classes and closer interaction with professors. Large public universities and large privates will provide better research opportunities, although you can often do research at LACs and get to know your professors well at larger schools. But generally it’s more or less true.
Many great LACs are in New England where it can be extremely cold and icy. Some are in the South, which has nice weather during the school year, and some in the Southwest/Southern California where it is hot/warm and dry. Many large state schools, especially in the South are very focused on sports like football and Greek (fraternity/sorority) live, which some love and some don’t. So if you think about what type of place might appeal to you, it will help you create a list that is more manageable.
Also, US schools are public or private. Most of the Top 20 or so are private (Harvard, Stanford, Johns Hopkins, etc.) but beyond that both publics and privates can be outstanding, world-class schools. In-state students pay less at public schools because state taxes pay some of the costs of the public universities in a state. So, for example, a student in Virginia will pay less than an international student or a student from another state because their family has been living and paying taxes in Virginia. Private schools generally cost the same for all students, although they will often (not always) provide less financial aid to international students.
Which raises the issue of how much you can pay. That is very important for international students. If you can pay most or all of the published international student costs (tuition, room, board, other), your college search will be different than if you will require lots of financial aid. In the latter case, you will need to focus on schools where you will most likely receive aid, which is often schools where you are a very strong candidate relative to other applicants. And even then it will be difficult.
In terms of rankings, to get a general idea of tiers, world university rankings really rank US schools differently than US rankings. World ones focus more on research, so LACs that are often considered great (the best) schools in the US are ranked lowly because the professors focus more on teaching than research. If you are looking to live and work for India, then world rankings might be more important. If you are looking to stay in the US (if that works), or just want to look at it from a US perspective, you might check US News College Rankings. These are very dependent on the criteria, and remember there are about 3000 schools, so #200 is still a really good school.
So think about those things. They will help you narrow your search. The great news is that there are many outstanding schools where students can get a great education. It’s not just Harvard, Stanford, etc. Good luck!