I went to Princeton for undergrad and had some graduate student friends. Princeton has a lot of resources, so there’s plenty for grad students (they would throw money at practically anything), but it’s very focused on its undergrad population. I imagine Yale may be similar, but can’t speak to it.
The grad life is relatively insular among departments or within grad student housing. Most of my grad friends happened to live off campus or were RGSs so don’t know much about on campus life. I imagine the grad college feels sort of similar to a small liberal arts college from a social standpoint. It is incredibly beautiful out there. There are some student groups that are specific to grad students or include both, and grad students definitely were into intramural sports.
Princeton grad school is going to be relatively quiet and focused. It’s a quiet/expensive town and you need to travel 1+ hr to get to nyc and philly. I knew some that loved the quiet and some who went to nyc every weekend. Depends on your personality and preference.