> I think that Venice, Rome and Florence are the most important cities in Italy

That's why you live there :-)

The worst thing about travel, is the travel part. When you find a fabulous City or Town to stay in, bargain for a week's worth of accommodation, and spend the saved cash elsewhere. Most important, you can get stop being a sherpa carrying around luggage, put your head down on the same pillow night after night, and get to know the people and the place. Once your familiar with a place, you don't need a map, you know your routes, you see people more than once, get to know there names; and they recognize you.

I'd suggest that in addition to two of the large cities, find one smaller one, like Siena, or Sorrento. The big cities are filled with lots of locals leading busy lives in a working city, and scads of tourists. Staying in smaller places will allow you to get deeper into the culture, develop acquaintances, and really understand Italia.

When you stay put, it's as if you've decided to live there, and these are the first days of doing that. It is immenseley rewarding after a few days. And your vacation time slows down. Anyone who is an experienced tourist knows that you pick a place and discover and enjoy it intensely, rather than skipping through places like your a rock star on tour. So, stay put in a great place. Otherwise, you'll be an expert in Europe's transportation system, where you'll spend many days. And that's where the dirt is, where the noise is and where the crooks are to be found. And that's where most bad experiences and frustration is found.

Have a great trip!