Well, I would choose Harvard because it is the most urban. Harvard Square is such a vibrant place and has so many food and entertainment options. Plus it’s across the river from Boston which is also lovely.
BUT Princeton does have a much prettier campus. Harvard isn’t really beautiful.
Yale is also really beautiful and scenic, so it would go after Princeton. And Stanford would be third.
And no, you’re not an international applicant if you’re a US citizen.