In this order, based on your criteria: Butler, Dayton, American, Miami-OH.
Butler is residential, has school spirit and sports, rather laid back.
Dayton is Catholic and like a smaller Notre Dame, excellent academics, traditions.
American would give you access to lots of internships, in fact one day of the week is set aside so students can go to their internship, it’s that common. Their academics are excellent especially in the social sciences and students come from all over the country to attend. But they’re not into sports.
Miami OH is larger than Butler, Dayton, or American, its campus is spectacular and there’s a lot of school spirit.
You should try and visit, do an overnight.