We spent 5 weeks in Florence last fall and it would almost get my vote --- we could easily have spent another 5 weeks there, especially if we could have kept our apartment that was on a non-touristy, pedestrian-only street.
Having just taken our 3-year-old grandson to Italy in March (he loved it, of course), I wonder about the very narrow sidewalks in Florence. In many places in the center of town, the sidewalks made it impossible for my husband and me to walk side-by-side for more than a few yards, or to stay on the sidewalk at all, so we were constantly stepping down into the street and then back up onto the sidewalk, and walking single-file instead of side-by-side. Not a huge deal for two adults, but I'm trying to imagine doing this with a small child. The sidewalks are not very stroller-friendly either, because various things like pipes project out from the buildings.
Of the places you name, I would choose Siena (where we just stayed for a week in early April) --- the streets and the Campo are much nicer and safer for a 3-year-old and it would be fun for him or her to look for the animals that represent each contrada. Easy to take buses or trains to other towns. The long, long, long escalator down to the train station and back up would be fun for a kid, too. "Historic charm, quaint alleyways, picturesque terraces" = check, check, check. Great food. Lots of art, including the floor of the Duomo, that a child would enjoy.
The only slight negative I can think of is that some of the streets are very hilly and many of the nicest apartments are up several flights of stairs. Our apartment was, and we didn't mind it one bit, but if our grandson had been with us, he would not have been a fan.
What an exciting adventure! Don't let anyone tell you that your child "won't even remember" and therefore why take him or her! Our grandson is still talking about Italy and, even if he wasn't, the point is how much he enjoyed being there every moment and that we got to share it with him.
