I need to spend a day in Milano with a couple of friends of mine,

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I need to spend a day in Milano with a couple of friends of mine,
the come from outside and I would like to show them around, but I don't know much interesting things to do/see.

So far I was thinking of doing some sort of tour like this

>Santa Maria delle grazie/ last supper/ Leonardo's home
>Sforzesco castle/ Parco Sempione
>Pinacoteca di brera if I figure out they're interested in art (maybe not)
>Montenapoleone and Via della Spiga
>Lunch in san babila

I've heard there's a place where they make a pretty good Pizza there, don't wanna take them to Luini because it's fucking overrated.

I'm trying to figure out how to walk them to the Duomo to get the best effect,
wich probably isn't from San Babila, I think it would be better either from the Gallery or Piazza dei Mercanti.

What do you think?
Anything else I could show them?