I lived in an apartment around 5 minutes from Bocconi with six other guys. I found the apartment on a Facebook group for exchange students and the rent was around 850 dollars per month. It was a very modern and clean apartment and I got to live with guys from Italy, Germany, Mexico and the United States. The cost of living in Milan is around 25% cheaper than Brisbane. I would say that the rent is about the same, but groceries, public transportation and entertainment is a lot cheaper.
Since I am an international student, I get a fixed amount every semester from the Norwegian government. I decided to use my Norwegian bank account since I was only going to be there for one semester. If you are planning to go on exchange for a longer period, I would recommend getting an Italian bank account. It was pretty easy for me to adjust to Milan and Italy because I had been there several times before and since I lived with six other guys I could just ask them if I was wondering about something.
During my exchange my heart started to beat out of rhythm so I decided to go to the hospital. The facilities were a little bit old, but they treated me very well and were very professional. For travel tips I would recommend going to Cinque Terre (on the coast), Nice (in France) and Venice (two hours east).
Do as much travelling as you can afford. I feel that the exchange experience has changed me a lot as a person and also a student. Since Bocconi was a pretty prestigious university in Italy and Europe there was a lot of good students and teachers you can learn from. You also feel like a stronger person when you have lived in a country that does not speak your native language. Life feels a little bit easier when you return to your home country. I would strongly recommend Bocconi as an exchange university.