Tip for budget travellers: Some of the trattorias and other eateries in Milan offer a set menu of the day ('menu fisso'), usually including two courses ('primo' and 'secondo') and a dessert or espresso. Although you have limited choice (typically 2-3 different dishes for each course) these menus are an inexpensive option (approx. 12-15 €) for having a proper meal and getting a taste of the Italian cuisine.
Another interesting option are the Happy Hours in the early evening offered by many lounge bars. Typically, when you order a drink you get a complimentary plate with small snacks ('aperitivo') or you can help yourself to the buffet at the bar.