I realize this is anecdotal, but it illustrates the point that it matters less where you go than how you do there.
I know of three very bright, high-achieving women (current seniors) who went to college with the intention of becoming doctors. They are all currently seniors. The one at Colgate got an early acceptance to U of Rochester med school her junior year based on how well she did in undergrad (https://www.swarthmore.edu/sites/default/files/assets/documents/health-sciences-office/Rochester%20Early%20Assurance%20Program.doc). The one at SUNY Geneseo got an early acceptance to Upstate Medical (https://www.upstate.edu/com/admissions/options/soph.php) with the caveat that she reach a certain score on her MCAT (she did). And the one at Williams is going to have to work for a few years before she can apply because she doesn’t have the GPA.
I’m sure there are many examples of the opposite happening at each school. Again, it’s what you make of your experience at your college.
And remember that med school costs LOTS of money, so unless you are super wealthy, keep that in mind as you consider undergrad costs.