<p>Texas A and M university: IN! But don’t go here, it’s a terrible school for someone of your caliber. 
Texas at Austin: In.
MIT (just applying for fun, no hopes.)= Very unlikely. Do you have any International Science Awards? Those could help.
Northwestern: No aid=In; aid=Unlikely.
Purdue: Same as above.
Should I apply at Princeton: Sure, why not? Princeton has the best undergraduate education in the world! I don’t go there btw 
As for your chances: Unlikely but you can try.
Stanford: Unlikely with or without aid.
Columbia: Apply ED and without aid, and you just might get lucky.</p>
<p>Good luck! :)</p>