Milan

The Duomo (you can go on the roof) and Galleria Vittorio Emanuele II. The Last Supper. http://www.vivaticket.it/index.php?nvpg[home]&op=cenacoloVinciano&change_language=1

Have you read any books, like Rick Steves' Italy, or watched any videos, so you have some clue, or are you just starting out?

When are you traveling - or as your message hints - are you there now?

Why did you pick Milan? Why did you pick Italy?

Are you there now?

In addition to sights mentioned, Castello Sforzesco (castle, grounds, museum), Brera Gallery, some importsnt churches.

Window shopping in Via Montenapoleone.

The cemetery there is quite impressive.

I took a 1/2 day tour scheduled thru Viators (a consolidator), it was partly by bus to get the general overview of Milan, then walking
We went into the La Scala opera house and spent time in the museum there, brief visit to the Duomo and we went back later to spend more time and go up on the root.
We walked thru the Galleria Vittorio Emanuele II shopping mall, around thru Castello Sforzesco, and ended at the Last Supper . The tour included admission to the Last Supper.
It was a great 1/2 look a Milan and then we saw many more things on our own.
I would also recommend the Cimitero Monumentale di Milano - it was really amazing and we spent
a lot of time there. Went by city bus from the Duomo area.

To minimize crowds and the humidity that comes with them, visits to the Last Supper are controlled, and you have to have an entrance time. Check Rick Steves' guidebook for details on securing a reservation.