This is about MIT in particular, but it applies to any highly selective college.
Remember that for ‘pre-med’ you can study any subjects- it’s just a group of classes you have to take. The keys for med school will be 1) GPA (both overall and in the pre-req classes); 2) MCAT; and 3) the competencies: What Medical Schools are Looking for: Understanding the 15 Core Competencies | Students & Residents
Whether you go to MIT or your state university won’t matter for med school admissions- but remember to factor in budget for both: avoid all debt for undergrad!!