If you are planning to visit the northern part of Italy in September or October, be aware that temperatures in October can be a lot cooler than in September. In Milan, for instance, the average low in September is about 52 degrees F, but it drops to near freezing by October. In September, bring a light jacket. In October, you will need a coat. Precipitation also varies. Octobers in Milan yield around 4 inches of rain, but Septembers average 2 inches. Pack rain gear, but avoid short pants, skirts and open-toed shoes.
In Rome and Florence, pack for less cool temperatures. Even in October, nighttime temperatures in Rome are unlikely to drop below 50 degrees F. Likewise, September highs regularly exceed 80 degrees F. Bring a mix of shorts and T-shirts for the daytime and long pants or tights for night. Rome is a bit rainier than Milan during September, averaging about 3 inches during the month. A raincoat is a good idea.
Naples and the surrounding region are similar to Rome during late September and October. Southern Italy is the rainiest region during September and October, averaging 3.2 and 5 inches, respectively. Definitely bring rain gear if you are visiting Naples, Sicily or Sardinia.