I've been to Italy three times and I have been all over the place. So many beautiful places that it's hard to name them all. I like the coastal towns that sit high upon the mountains overlooking the Med on the west side. Amalfi coast is absolutely beautiful, Positano, the Isle of Capri, and Tuscany. Venice is a very interesting place, at least for the first time. Extremely touristy and pricey! Rome is great for the history, but dirty. The Colosseum and the Vatican are a must, but long lines to get in. Pompeii is very interesting if you are a history buff like I am.
Get a car service. Best thing we did and they can take you to the best places. Easy to get around in Italy due to excellent train service....for the most part. Be aware of what you are charged when buying anything, food, clothes, etc. Inflated add ons are rampant. The laws in Italy are very lax and sometimes seems non-existent. Also, they ordinary citizens don't particularly like Americans. Look to be "bumped" into several times while walking the streets of Rome. After, the third time one day, I grabbed the guy. He just jerked away and went on.
I think everyone should go at least once, but certainly go for at least two weeks and travel around. It's hectic that way, but it's the only way to see as much of Italy as you can.