Italy in 2-3 days
If you've only got a few days in Italy you have to visit Rome. Base yourself in the centre of the city (perhaps near Piazza Navona). It might cost you a bit more in accommodation but you're then free to explore the city on foot. In a couple of days you can take in the Vatican City, throw some coins into the Trevi Fountain, pick a fight with a gladiator at the Colosseum and check out the Roman Forum.
In 7-9 days
Begin your trip in Naples and visit Pompeii, a Roman city buried by Mt Vesuvius in AD 79.
The next day, jump on a ferry and make your way down the Amalfi Coast. Stay for a few nights in Sorrento, Positano or Amalfi. You can do day trips by bus or ferry to the surrounding towns or simply sit on a beach and relax.
If you have expensive taste head over to the Isle of Capri for a day where boutique stores line the streets.
Make your way back to Naples or Salerno where you can catch a train to Rome. Spend the remainder of your days in Italy's capital wandering the streets (see Italy in 2-3 days above), taking in the sites and eating too much Italian food.
Two weeks +
Start with the 7-9 day itinerary and then make your way north to Florence. Base yourself here for at least three days so you can take in the museums and galleries. You could also make a day trip to Siena which is a wonderful town in which to wander.
From Florence, jump on a train to Venice. It's not a big city, but it is certainly one of the world's most unique, so give yourself at least a couple of days to get lost in its streets.
From Venice, head west to the Cinque Terre — a collection of five villages on the Ligurian coast. Base yourself in Vernazza, arguably the most attractive of the villages, which has plenty of accommodation and great restaurants. During the day you can walk between the villages and it takes about four hours on foot from the first to the last village. The Cinque Terre gets quite warm in the summer, so if you've got time give yourself a day to sit by the sea.