If you are studying in a private international school you should have advisers that know where the top students from your school have a good chance. Start there. Of course add colleges that interest you. Find out about colleges so you can choose some yourself. Colleges here have their own personalities and features.
@momrath misspoke about need blind colleges. Many colleges are need blind. Almost all public are. They will admit you and just give you a large bill. When people talk about the six colleges for internationals, those are need blind yes but most important they will ‘meet need’ for internationals. Many others privates are ‘need aware’ for internationals which means they may not admit if they don’t think they can give you enough money, or full payers may have a better chance, or you may get in if you need less aid. In other words, there is limited funds to go around for internationals, you may be accepted with aid or you may not and you chances could be better not asking for aid, but only if you can afford to go without aid…If you can’t afford to go without aid it is better to ask and get rejected. If you get in you may get some if they think you have need.
So
need blind you can ask for aid - publics (although most will not give aid to internationals some will), Harvard, Dartmouth, MIT, Amherst, Yale, Princeton
need aware - don’t ask if you can afford it, ask if you can’t