1: Don't Try To See It All
This is the biggest mistake that most travelers make. Think about trying to see your own country in one fell swoop; it can't be done. Instead, concentrate on seeing a few things and seeing them well. Don't make checking an item off a list a substitute for getting a feel for the spirit of a place. This is why my Italy Photography Workshops seek to provide an immersive experience for the participants. My goal is to help photographers really see, experience and photograph the essential aspects of a particular Italian location.
2: Go Off The Track
The farther you get away from large towns and cities, the more "pure" your Italian experience will be. I am not suggesting that you ignore the great Italian cities, but rather that you balance a visit to, say, Florence with a few days in the Tuscan countryside. In other words, watch where the crowds go and then walk or drive in the opposite direction. This is exactly the strategy I employ in my Photo Workshops - we get to see the sights everyone wants to see, but we really do get off the beaten track as well.
3: Get Up Early & Stay Up Late
The light is so beautiful in the morning (great for photography), and the crowds that throng to popular places don't arrive until after they've had a proper breakfast. Getting up early gives you quiet time in a place that you can't get any other way. Staying up late assures you that you won't miss the wonderful social time that Italians have late in the evening. You also will be more tempted to eat your evening meal when Italians do; sometime around 8:00PM or later. Of course, this means that you might want to reserve some time in the afternoon to have a nap, just like many Italians do.
4: Eat With The Locals
Italy offers one of the most satisfyingly wonderful gastronomic cultures on earth. You can eat well (really well) almost anywhere. I frequently ask people who work where I am staying where they go out to eat. Asking the desk clerk works, but asking the gardener is even better. I ask them where they would take their families for a good dinner. What you'll find from their responses is that you can eat great food for small money. Even if you are too timid to ask someone, see if you can figure out where local folks eat by going a bit out of the way and looking for local cars or foot traffic.