In Milan I enjoy fairly traditional local food at places like Osteria del Treno (between Piazza Repubblica and the Stazione Centrale) and Rovello 18 (not far from the Castello). In the winter you can get traditional Milan/Lombardy dishes like cassoeula and bollito misto and pair them with Northern Italian wines.

There are plenty of good high end places in Milan in a variety of styles including Cracco Peck, Aimo e Nadia, Gioja (vegetarian high end concept food), Don Lisander and Sadler to name a few.