I lived in Orviteo for a year during college, it is located in the region of Umbria which is in between Florence and Rome. If you have the time it would make for a good couple of days. There is some great history there, you will especially find a lot of sites concerning the Etruscans which is a civilization that predates the Romans by a couple hundred of years. Orvieto also has some great wines and there is a really cool wine bar that is built beneath the city. Another great Umbrian City is Perugia which is the capital of the region, you are still able to see the original Etruscan gates there. Perugia is also known for their chocolate. The last city(which is more of a necropolis) I would recommend in the region is Cerverteri. It is a UNESCO world heritage site, there are over 1000 tombs that you can see.
Venice is a great city but a tourist trap you can stay in Lido which is much cheaper and very close. There is an old monastery called San Lazzaro degli Armeni in the bay near Venice, they have an amazing view and museum.
Some of my favorite sites in Rome were the Domus Aurea, which is under the Baths of Trajan(check out the baths too!). The Trajan markets and his column detailing his victories in battle(the column is a must see). The temple of Jupiter and the Roman forum, which was the place Cicero's hands were nailed to. The Vatican museum is also a must see. There are a few little churches around Rome that have Caravaggio's in them, they are worth looking for.
If you have time to make it down south to see Pompeii make sure to see Capua on the way which is a very will preserved city, it is also where Spartacus the TV show took place. Naples National Archaeology Museum is a pretty mind blowing place, they have the Alexander Mosaic which is worth going just for that. One of my favorite cities in the south is Paestum which was originally a Greek colony. You can see the Tomb of the Diver there which is one of the few well preserved Greek fresco's. There is also a pretty amazing Greek temple there that is in great condition. The last city I would recommend is Amalfi this picture explains it all.
Some travel tips in Italy: The trains suck so expect delays. The Rome Termini is full of Gypsies so mind your wallet. The bus from the Rome Termini to Vatican City is full of pickpockets. The closer restaurants are to the main sites the more expensive food will be. Beer is cheaper then soda, take advantage of it. You get charged for bread at restaurants, but on the flip side tips are not expected. Italians do not like to queue. You buy slices of pizza by the kilogram not by the slice. The people get nicer the further south you go. Naples can be very very sketchy at night. Have a great trip!