There are very few cities in the world with as much history, historical buildings and artifacts as Rome. A great example is the Colosseum... But Rome is not just history, it is also the political capital of Italy and offers great eating places and places to watch-the-world-go-by.
The city of Venice needs no introduction, because it is one of the best known and beloved tourist cities in the world. Major attractions are the Gondolas, the many Bridges and St. Marc´s Square. Once a year there is also the traditional Carnival with beautiful masks and dresses. A few times per year there could be flooding...
Florence is a city with a long history. It was the home of Michelangelo and Leonarda da Vinci. The two major tourist attractions are the Dome and the bridge, but we can also recommend the delicious ice cream of which there are many flavours here!
Pisa and its Leaning Tower... How many people supported it from falling down or embraced it?
Naples (Napoli) has a well-kept, old inner city. It is also close to the Vesuv volcano with Pompei-ruins and the Island Capri. Pizza Margarita was "invented" here.
The Amalfi Coast is very picturesque and lies on a steep southern shore of the Sorrentino peninsula.
Milan is the "capital" of Northern Italy and a very influential city when it comes to economy, fashion or music. A highlight could be a visit to the Scala, if you can get tickets,
Palermo is the capital of Sicily, the large island in the South. The people call themselves Sicilians rather than Italians. Palermo is known for the large cathedral, Sicily is known for wine, olives and ... the Mafia (~movie The Godfather).