I suggest that you apply to all schools that you dream of attending & hope for merit aid to fill the gap between need based and out of pocket. I also strongly suggest that you look for small private schools that are not necessarily “name brands” - they are often great schools with full time professors teaching and mentoring undergrads. Small class sizes and very engaged student populations. In the Ivies, you are often taught by teaching assistants/grad students as the ivies reserve much of their teaching talent for the graduate level students. Better to go where you have a full ride for undergraduate studies and head to the Ivies for grad school.