One of my favorite historical building from Milano, 

'Un posto a Milano' is a restaurant and cafe in Cascina Cuccagna, an ancient building which is dating back to 17th century. It was originally intended as a residential farmhouse and it is now completely surrounded by the city of Milan.

Art and design museum in the Parco Sempione. Some permanent and some rotating exhibitions. Definitely visit the Casa Lana installation and the Italian Design permanent exhibit.

Small home/gallery space featuring various works from the Memphis movement.

Giacomo ristorante, bistrot... They are all located on the same street, Via Pasquale Sottocorno, but the rosticceria is the more, let's say, "easy-going" (and the cheapest) of the three. It's a good place for lunch and dinner - ask for a table at the "giardino interno".