Do the differences in general education requirements matter to you? You may want to look them up.
Providence is better than Princeton or New Haven any day. Great town, great food, state capital, there is a lot going on there.
I would suggest Yale or Princeton. I have been to both New Haven and Princeton several times, and the surrounding area and safety is not a legitimate reason to turn down Yale. Downtown New Haven by Yale is super nice and actually quite impressive. Princeton NJ is equally great. Both campuses have storied histories and beautiful architecture. Yale may have more traditions, but both have perhaps the proudest alumni in the world. Both excel in every field. When it comes down to it, you are deciding between an urban campus and suburban campus. Both will be safe, beautiful, and full of fun things to do. Where would you be most excited and comfortable?