Being European, Italy is my favourite place and I've been there umpteen times. I lived in Switzerland for 10 years and used to go to Italy on day trips as well as vacations. The atmosphere there is so friendly and happy, I especially love the early mornings when the life starts outside, it's not uncommon to hear people sing when they go about sweeping the streets or shouting to another in a friendly way out the windows of the houses.
And the food, it's to die for. Simple but oh, so tasty.

Milano:
The Duomo (Cathedral), the most extraordinary Italian late Gothic art.
Piazza Duomo in front of The Duomo.
The Galleria, one of the first building in Europe built in glass and iron (facing Piazza Duomo) and it's a meeting place of the Milanese. It's got a famous historical restaurant there. Plus you've got the operahouse "La Scala" at the other end and you can always see people in all their finery at The Galleria before going to the opera.
"The Last Supper" by Leonardo da Vinci at Santa Maria Delle Grazie.
For a spot of shopping (fashion, books) there are the famous streets near Piazza Duomo, "Corso Vittorio Emanuele" and the more exclusive "Via Montenapoleone". Milano is "the" fashion city of the world.

Firenze:
Michelangelo's David at Accadeia Dell'Arte del Disegno.
The Uffizi Gallery is a MUST! Reserve tickets in advance if it's high season as the waiting time during that season can be up to 5 hrs.
The famous bridge "Ponte Vecchio" over the river Arno. When the Germans blew up the bridges along the Arno during WWII, Hitler ordered not to blow up "Ponte Vecchio" as it was too beautiful.

Venezia:
The canals, the gondoliers, Piazza San Marco surrounded by impressive buildings. There are two enormous columns of granite welcoming visitors by boat. The two columns were also the preferred place for public executions ;o)
Murano, on Piazza San Marco, famous for their glass art. They've been making glass art for over 700 years there.

In Northern Italy there are the lakes Lago Maggiore, Lago di Como, Lago di Garda and the area is breathtaking. If you drive there in the hills on the narrow roads (or anywhere else in Italy for that matter) you will notice it is custom to honk your horn before you go around a bend as the roads often are so narrow that 2 cars hardly can pass. And the Italians are fast and impatient drivers, you've been warned ;o)
The tunnels you drive through around Lago di Garda are quarried in the mountains and were done by prisoners of war. Fascist dictator Benito Mussolini had his mistress stashed away in a beautiful villa along Lago di Garda, Greta Garbo had a another beautiful villa in Malcesine.

For countryside there's Toscana with beautiful old villages scattered around.

I better stop before I get carried away ;o)