Hi Mary
I did this trip last year. I went in October, and the temperature was just right for city visiting. I think Spring would be OK too.
I loved it all, though it is a very busy itinerary; lots of early starts.
The three main city visits were very well organised, and set us up with a real practical approach for getting the most out of the city in the time available. I particularly loved Florence, so much so that I was inspired to go there again, this time for a weekend on my own in April.
There were also lovely trips into smaller towns/cities like Bologna, Lucca and Orvietto which were a delight.
Hope that helps
Jackie