Yale is mostly self-contained. Few students have cars and public transportation options to Hartford are limited. Students who wish to escape are most likely to take a train, either south to NYC (they could also go to Bridgeport, although I never heard of any doing so when I was a Yale student myself) or north to Boston, with the possibility of stopping in Providence, RI.

And, incidentally, the St. Thomas More Center for Catholic students and faculty at Yale apparently has a strong program. I have no current personal experience of this but read about it in the newsletters they send to alumni/ae.