The view from the roof of the Duomo, in all directions, but especially north, is a treasured memory from a 2 week trip to Italy. The wood statue in the church, also. I get "Not another Church" but it kinda is the 4th largest church in all of Catholic Christendom (through some manipulation of boundaries of consecration, sure, but still). It took 500 years to build (due to invasion after invasion) and would have taken longer if they'd done the whole deal on the stained glass and not "tupperwared" out. No matter how churched out you are, the Duomo di Milano is worth an hour or so. A mountain of marble from Carrara, a monumental achievement in conquering the weight of that most impractical substance.
Have a nice meal. Lombardian cuisine is so not Tuscany. It's so much tied to the various invasions, of Spaniards, of French and mostly of Austrians.
If you're remotely interested in opera, a tour of La Scala can be arranged. If you're remotely interested in luxury shopping, Milan is your town.
Wife was not so gaga for the whole experience that is involved in seeing the Last Supper. I found it amusing (the serial dehumidification), but wife wanted to get on with it. It's not so much the fading, it's that it's a lot of pomp and circumstance and hype for something that was falling apart six years after it was finished because of an odd frescoing experiment. It's an important art work, but there are much better preserved Michelangelo works around the world.
The Brera neighborhood is nice as is the gallery of the same name within.