Recommended sites to see in Milan?

The Duomo and its Rooftop
Brera Gallery and the area around it
The Sforza Castle with Michelangelo's Pietà
The Scala Opera House and the Museum
The Technology Museum if you have kids
If it wasn't for the draught I'd tell you to have a walk in the Navigli District and dine there, but they are slowly emptying the Canals to save the crops.

Be aware that the airport train to MXP that departs from Milano Centrale takes 15 minutes more than the one from Milano Cadorna station.

Adding to Dario's list, Basilica di Sant'Ambrogio and Basilica San Lorenzo Maggiore.

https://www.yesmilano.it/en/see-and-do/venues/basilica-di-san-lorenzo-maggiore
https://www.yesmilano.it/en/see-and-do/venues/basilica-of-sant-ambrogio

Of special mention at Sant'Ambrogio are the 11th and 12th-century carved column capitals in the arcaded portico, no two alike. These are not my shots but will give you a sampling:
https://www.flickr.com/photos/prof_richard/48807675182

And while I sadly haven't been there yet myself, this one is on the next-time list; a wealth of sculptural material for shutterbugs (google up some images):

https://www.yesmilano.it/en/see-and-do/venues/monumental-cemetery

You all never cease to amaze me with your knowledge and generosity! Thank you so much! Hopefully one day I will also be in the position to make recommendations like these!! Caio!

Second vote for the monumental cemetery --- we spent most of a day there and didn't see even half of it. Incredible, over-the-top, often life-size or larger, dramatic, many sad but also some unintentionally funny sculptures. Best monumental cemetery we've seen in Italy (so far).

I'd say skip the interior of the Duomo and just go up on the roof, if you are pressed for time.