You can do Rome in 2.5 days or 3. It is a great city to tour but at this time of year if you spend more than 3 days there you are missing out on some great places to visit and spend your time. We usually take a Fast moving Train down to the Amalfi Coast and spend a day in Positano. Train to Salerno, Ferry to Positano, Ferry to Sorrento, Train back to Rome. Your GF will love it. One day trip up early back 13 hours later or spend the night. It is one of the most Vertically built cities in the world.
Florence is the best city to tour for history and day trip out of this area is where we will easily spend a week and visit all the cities in the area. I saw Carlos Santana in Concert at San Lucia in 2007 there on by luck.
Lake Como is another adventure as well as you can day trip into Switzerland by train and stop n go type scenario.
Venice is awesome during the week and go to the Bra Bar for sure tell Fabian I said hello.
We go for 21 to 25 days, 7 trips from US alone and months living in Italy and visiting from other countries. We go to Europe Italy is always on the Itinerary.
My opinion is you are going to miss the game. Enjoy your trip.