I think we already discussed this http://talk.collegeconfidential.com/financial-aid-scholarships/2143704-merit-scholarships-at-t20-schools-p1.html
You can check the website of each one to see if they offer any merit - that shouldn’t take more than a few minutes of your time. Ivies do not offer merit scholarships, period, so you can eliminate those eight off the bat. Off the top of my head, check the scholarship webpages of U Chicago, Northwestern, Duke, Notre Dame, JHU, Vandy, Rice, WashU, Emory, CMU, USC. The big caveat is that they are all reaches even for admission, so any applicant’s chances of significant merit may be in super-reach territory.
Good point above about LACs, as there may be more top-20 LACs that offer merit than top-20 national universities.
In addition, the further one looks down in rankings from 20-ish to 50 and beyond, the more likely one might find the possibility of merit and in greater possible amounts.