Stayed at Milan Marriott several times, and they recommended several places to eat, but we found that walking to nearby sidewalk cafes are also more of trend of locals. The hotel can give you directions. It's kind of fun to walk along the main street with shops, check out the variety of foods, and stand up to eat, at least on one occasion.
Convivium- Via Ponte Vetero 21—Brera area, great
Obika=Via Mercado 28—Mozzarella Bar- also in Rome, Florence
Osteria La Carbonella Da Santo- nice quiet, family run,
Al Pont Du Ferr- on the River
Trussardi – by La Scala- nice bar, café, formal dining upstairs
Noon- bar, by Cadorna station
Important to remember, many of the bars, like Noon, and also Obika [which is restaurant] put out huge buffet at happy hour which are complimentary w/ a drink. You could really dine off the buffet, but what would be the fun in that.