All schools (except maybe HYS) use merit money to attract top students, though some are more generous than others. If you really have HYS numbers, there's the possibility of money from almost all of the T-14 and below. Columbia has the Hamilton (full tuition), which is given with your acceptance. NYU has several scholarship programs that you apply to with your regular application that are up to full tuition. Chicago doesn't give full rides. I think they stop at 64k, but you can check lsn to confirm.
Penn and Mich both have scholarships that are up to full tuition that they invite you to apply for after you're accepted (Mich is the Darrow, not sure about Penn). UVA has various Dean's scholarships that they award after acceptance. From there down the sky is the limit of up to full tuition (or eve more), depending on how much they want you. However, money can be a bit of a crapshoot (eg, I got nothing from Penn or Northwestern but practically full ride from NYU). My best advice is to cast a wide net if you're looking for big money. You have a better chance of getting money from a school that you like and can also use offers to negotiate for more.