The school that I am most familiar in this area is John Carroll University, where my older son went for pre-pharmacy/chemistry. It’s a 3000+ Jesuit university in the suburbs that has a very well regarded department in Exercise Science and Sports Leadership (just google “John Carroll” and “NFL” if you want to see why). The proximity to all the major sports teams in Cleveland makes it easy for the kids to get internships with pro teams.
I know you mentioned that you don’t want a Catholic school, but Jesuit schools tend to be more open than Roman Catholic schools.