Someone who is not religious may not enjoy being at Notre Dame.
Also, as a study-abroad student, prestige doesn’t matter. You want to go where you’ll be able to study your coursework and be in close proximity to historical sites.
I would say Mason or Richmond would be some of the best choices from that list. I don’t know Temple that well, but from people’s descriptions, that definitely would be a good option too. Mason has the easiest transportation to DC, since there is a campus shuttle directly to the metro. From Richmond, you can take the Amtrak train to DC; it’s about 3 hours I believe. The Amtrak station is very close to campus (you can actually hear the trains at night on campus).
I’m actually a current student at Richmond, but I live very close to Mason (I have all my life) and took a couple summer courses there. In terms of academics, Richmond is much more rigorous and is very strong, especially in the humanities and international studies (its also fairly selective; approx 30% acceptance rate). Mason is still primarily a commuter school, but they have a growing community of students staying in the dorms.