While you will be a competitive applicant, with that budget I don’t think you will be able to afford most of the colleges that you listed.
Yale and Columbia only give need based aid, and with your Family’s income you won’t qualify. Why do they only want to pay 20K a year? With that budget you’ll need a lot of merit aid.
Vanderbilt should be a reach, because it would only be affordable if you get their full ride scholarship, and obviously that is very competitive as well. I think it is open to international students as well, but double check that.