Italy is a fantastic country with history dating back in the written sense longer than nearly anywhere else in Europe. Rome is a must visit. Florence is a gem of art and architecture. Venice is unique, and while I would not want to live there, is worth a stop. Milan? I'd skip it unless you really, really want to see either one of the most amazing cathedrals in the world or The Last Supper in person.
An interesting side destination in Italy is the tiny Republic of San Marino. With time and a sense of adventure it's worth a day or two.