My D21 (premed/biochem) was looking for merit, strong prehealth advising, research and service opportunities and preferred a LAC or mid-size. Here are some schools to include in your research. These are a range of sizes and selectivity… remember if merit is the number one goal you may need to compromise on other preferences. Any school that requires merit to attend should be considered a reach regardless of admissions probability.
Washington & Lee - Johnson scholarship (full ride) and some targeted full tuition merit scholarships
Davidson - Belk scholarship and James B Duke (the Belk requires a nomination by your school, I believe)
Rhodes
CWRU
Duke - Robertson scholarship (requires a nomination) and others
UNC - Robertson scholarship (requires a nomination), Morehead-Cain and others
UVA - Jefferson scholarship
I would also include some of the auto-merit schools like Alabama, Miami-Ohio, etc. as suggested by others.
Your instate publics may end up being the best financial fit, but as long as you have those safeties there’s no reason not to try for these competitive scholarships. It’s a lot of work applying for merit and there are typically earlier deadlines so plan accordingly so you don’t burn out.
Good luck!