Being a broke student, I ate from supermarkets most the time in Italy, especially in Venice, as prices were ridiculous. As far as Milan, shopping and eating is better, trendier, and more affordable in Navigli(southern area where a lot of college students hang out). My friend and I had a great meal with salad, bruscetta, entrees, and soft drinks for under 50 euro.

I would recommend wikitravel.org to find a slew of eating/shopping at all price levels