Although it's tough to tear yourself away from Umbria, in fact it's easy to visit other parts of Italy. Florence and Rome are just a couple of hours away, so a day trip is easy. The other destinations will probably involve a longer stay, but trains are fast and inexpensive.
Florence - the jewel of Renaissance Italy Florence is a World Heritage site for good reason - its artistic and architectural heritage, its sheer beauty, and the wealth of monuments, museums (including the Uffizi Gallery and the Pitti Palace) makes it a must-see. It's easy to drive to Florence, but traffic in the city can be dreadful. Fortunately, the train from Perugia takes less than two hours and costs between $15-24 each way depending on class of service. Visit the Duomo, walk through the many piazzas, spend time in the Boboli Gardens, and then treat yourself to the authentic Bistecca a la Fiorentina and a glass of Chianti Classico.
The Colosseum. The Forum. Capitol Hill. The Pantheon. The Vatican. The Sistene Chapel. St. Peter's Basilica. The Campo dei Fiori. Piazza Navona. The Piazza del Popolo. The Spanish Steps. Villa Borghese. Where to begin? Rome is a very accessible city, easy to walk and with a wealth of must-sees in relatively close proximity to one another. There are intimate cafes around every corner, plenty of wonderful places to eat (don't neglect the Roman classics, carciofi alla romana and spaghetti carbonara). It's worth a side trip to Fiumicino, the little fishing village just outside the Leonardo da Vinci airport, and Ostia Antica, where you can take a leisurely stroll among ancient Roman ruins.
Pompeii is a partially buried Roman town near Naples that must be seen to be believed. Both Pompeii and Herculaneum were destroyed and completely buried during a catastrophic eruption of Mount Vesuvius that lasted two days in AD 79. The town was buried under meters of ash, and was not rediscovered until 1749. The excavation has uncovered a detailed snapshot of daily life in a Roman town. The forum, the baths, houses and villas are very well preserved. To get to Pompeii, take the train to Naples and from there take a local train to Herculaneum. It’s a short walk to Pompeii. Wear sturdy walking shoes and bring water, since you will want to spend several hours walking through the ruins and imagining life in the first century.
The Amalfi Coast
The Amalfi Coast is a fabulous stretch of coastline in Southern Italy, a popular tourist destination. The climate is Mediterranean, with warm summers and mild winters. The only land route is the treacherous Strada Statale so you might prefer to take the train. Take a train to Naples, then on to Sorrento with its sea cliffs and luxury hotels. Don’t miss the limoncello liqueur for which the town is famous. Continue to Positano which is located in one of the most beautiful valleys of the Amalfi Coast, opening onto an equally magnificent stretch of coastline. Built vertically on the face of a cliff, it is a pedestrian town with many stairs and pretty pastel colored houses.
Venice is known as one of the loveliest cities in the world. It is virtually the same as it was six hundred years ago. The world’s only pedestrian city, is easy to walk. There is also the possibility of getting around on the vaporetti (water buses) and water taxis. Be sure to visit the Basilica di San Marco in the Piazza San Marco, and the Palazzo Ducale, also in San Marco Square. A special guided tour will show you Casanova’s jail. Take a side trip to the island of Murano and visit the Museo del Vetro, where you can see the typical glass for which the place is famous. The Rialto Market and Rialto Bridge provide all you need for shopping and dining.