I don´t think that it´s really something for everyone, but: the cemetery of Milan is absolutely great. There are family tombs you can swear this are little churches.
Piazza dell Cimitiero
(see also the travelouge)
Have an espresso in the cafe atop the department store, La Rinascente. The close-up views of the Duomo are spectacular. It is also a place to get in from the cold. And there are public bathrooms.
Museum of criminology, you can see a lot of instruments of torture.
You´ll find it in front of the church Sant´Ambrogio
There is a nice monastery in Pavia some kilometers out of the city. Great and real authentic atmosphere.