The best thing is its campus: It is the perfect blend between living in a city, without having it be too overwhelming such as NY, and without being stuck in a small town. There is also an actual campus, but it is not a closed campus (like Columbia) or a completely open one (like NYU), which creates a sense of belonging and community at times. All of your classes are within 2 to 10 blocks, and there are a lot of shops around. Not to mention that all the buildings are historical and beautiful.
However, it is easy to get stuck in a rut and never go "off campus" and into the city, staying within the confines of some 10 blocks or so. The good part is that the city is only 20 blocks away, east and west, and there is public transportation within the city as well as to the suburbs. Philadelphia is not the most welcoming city, but once you get out and explore you will find neat hidden places that are not commonly frequented by college kids.
The second best part goes hand in hand with the campus: you have the option of living "off campus" without actually being off campus. You can live within one or two blocks of the usual dorms and buildings, pay the same or even less than a dorm, and have your own apartment with your own furniture, and make it feel like a home. Obviously university city prices are inflated, but in general apartments in the city are expensive.
The worst part about Penn is the administration. It depends a lot in which school you're in (SAS, SEAS, Wharton, etc) but in my experience I have had the worst and the best advisors. The admin staff in general does not care about you, and makes every effort to make you feel as uncomfortable and pissed off as you can. Not to mention that there is not one semester where I file a petition for something, and only one has been accepted.
The facilities in general are very good. I use to think the dorms were awful, but then I saw other universities' dorms. We have an awesome gym a few blocks away from anywhere, a huge library, another library, lots of study areas, and *most* of the classrooms (ie Wharton) are well fitted with technology, although the interiors are sometimes very unwelcoming.
I feel the UA, or undergraduate assembly, definitely works and listens to the students, implementing a lot of their suggestions within a year or two. There are a lot of groups on campus, although the joke is that there are more accapella groups than any of the others combined.