NYU for business and GWU for politics/IR are both very competitive admissions, both are need aware (NYU for internationals, GWU for everyone), and neither meet full need. You can research further on the college pages about college scholarships, realizing they will be competitive and that while your resume looks impressive, so do many, many others they get. I am not trying to be harsh here, you just need to be realistic. By all means apply to these schools - you may get in and you may get good funding - but you really need to have a good back up plan for if you don’t. If the colleges that we would consider good backup are not prestigious enough for you (I’m not being sarcastic, I also come from a foreign country and know well how name recognition works at “home”) it may be better for you to go to a domestic college, do really well in undergrad, and then come to the US for postgrad. This is quite a normal route - If you look at the statistics, foreign students tend to be much better represented at postgrad than undergrad for the higher ranked colleges.
By the way, even if you can apply undecided, at least at these two you still have to apply to a particular school (for example you can apply undecided to NYU CAS, but that still puts you in CAS, as they admit by school not by major. If you apply undecided to Gallatin, I can almost guarantee you you will not get in. I can’t remember if you can apply undecided to GWU but again you have to apply to a particular school within GWU. Unless it’s changed, American is one where you apply to the college as a whole and not a particular school within it. American is suburban rather than urban, very good for IR, not so sure about business, does not have a great reputation for good aid.)