Very near the centre of Milan are the Colonne di San Lorenzo - these are in walking distance from the duomo - just go down Via Torino and keep walking - it is were all the students/hippy or in Italian "grezzo" types hang out.
I thought they were really beautiful anyway as they are roman columns in the middle of the city with a beautiful Greek style church in the centre. There is a tram line which runs past them and it feels you are taken back many years. In the summer you can take aperativo outside and you should really go down there just to people watch.
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.