The best way to get a scholarship is to apply to schools that are generous with them, of which there are very few.
Washington University - some full tuition and half-tuition scholarships, maybe around 10?
Vanderbilt University - decent number of students get some merit-based money
Emory University - a handful (maybe 5) of full-tuition scholarships, no other merit money
Case Western - 15-20 scholarships ranging from $20,000 to full-tuition
UPitt - from what I hear, decent amount of people get merit based money from them
UChicago - very generous with merit based money compared to most other schools
UMich - dunno anything about how much, but they have at least some merit-based scholarships
And don't forget the schools that are already cheap to begin with, namely:
All your state schools
Mayo Clinic
Baylor