Italy is AWESOME. I love traveling there. I went in May 2006 by myself and LOVE LOVED it!
Touristy places to see:
Rome (Colosseum/Palentine Hill, St. Peter's Basillica/Vatican, Pantheon, Spanish Steps, Trevi fountain etc) When you go to the Vatican, get a tour - it adds SO much more than just going on your own. I've been 3 times, unfortunatly I can't remember any of the companies I went with. Ask at your hotel for recommendations though. If you can find a good walking tour of the city, I'd suggest you take it. There is SO much history that you can't get out of a little blurb in a guide book
Florence - Uffizi, Palazzo Pitti, Duomo, Ponte Vecchio, Santa Maria Croche (has Michiavelli, Galileo and Michaelangelo's tombs) - If you can find a walking tour of the city, again take it, but don't waste your money on a tour of just the Uffizi. Most tour guides brush over a few sculptures/paintings and just skip to David (you can get this info from a guide book)
From here you can hop a train to Pisa - make this a day trip, there really isn't a ton to see besides the tower. I didn't go up in it, because they limit the ticket sales and the line was a mile long
Venice - St. Mark's Cathedral, just wander around here, it's pretty sweet. I got lost though because one canal looks like another, so take a map!
Less touristy but awesome places:
The Cinque Terra - Near Florence, a series of 5 towns that you can hike between (or take the train if you prefer). It's a pretty intense hike getting rather narrow in places or steep steps in others. It took me about 4-5 hours from start to finish. Well worth it if you can do it! This place is gaining in popularity though. Absolutely beautiful
There's also some awesome beaches here (pics 1/2)
Milan - not really too touristy because people tend to flock to Rome/Florence but it has one of the most awesome cathedrals that I saw while I was there!
Naples really didn't do much for me, I wouldn't suggest it for you. It's kinda the armpit of Italy, but it makes a good jump-off place for Capri, Mt. Vesuvius, Pompeii and Herculano
Capri (island near Naples) - known for it's grottos (caves) that you can swim in. I didn't do that, instead I took the forneculum (sp?) tram thing up the one side and this scary bus down the other to the beach where I spent the day. Awesome. (pics 3/4)
Herculano - ruins that were covered in ash when Mt. Vesuvius erupted. Because of the ash most things were preserved VERY well. There was a lot of original tiling and even some wood which was pretty sweet. I didn't go to Pompeii but the people from my hostel that I went with told me that Herculano was in much better shape and a lot less crowded than Pompeii
Also near Naples is Mt. Vesuvius - You can climb up to the top of it for a nominal fee (i forget how much) but it was sweet sitting on top of a LIVE volcano! (last picture is me on it!)
Amalfi - very beautiful on the coast, but it is a PITA to get to by train. I also might have just screwed that one up when I was getting there though
Once I was there it was pretty - but not too much to see besides chilling out on the beaches.
Ok that should give you enough for a start! I went in May, and didn't have any issues with Holidays or events. It's a great time to go as it isn't quite hot yet and is isn't quite "tourist" season so things aren't totally expensive. I'm going to post some pictures because i'm all excited for you!