We went during the month of April and it was great. My main reason for choosing April rather than the summer was because I tend to get bad headaches when the air temperature is hot, and that's no way to spend a vacation! There were areas that were still crowded (Trevi Fountain comes to mind) and it was too cool to enjoy the beach in Palma de Mallorca, yet it was a great time to go, overall. No other big ships in port, either.
baby doll, from the average temperatures from weather.com for Rome
, it appears that late October and November are great, with average highs in the 60s to low 70s Fahrenheit. Low temperatures in the 40s-50s, but those are overnight, when you'd be on the ship. This is pretty much what we had in April a couple of years ago. When going ashore, we wore jeans or khakis, short-sleeved shirt, and light jacket...and, most importantly, comfortable walking shoes. The jacket and pants are also perfect as you'll need to have shoulders and knees covered to enter most places of worship.