Rutgers has a BS/MD program open to freshmen on their Newark campus with Robert Wood Johnson, but the deadline for that passed this year. You can also apply for a separate program as a sophomore(I think?) at the New Brunswick or Newark campus. They have a similar curriculum as far as I know so you should definitely look into it.
The Newark campus is like 20 min from NYC through NJ Transit while the New Brunswick campus is about an hour away near Central NJ.
For the sophomore program: Rutgers HPO
For the freshmen program: Pre Health Studies