I'm considering a 6 week sabbatical for next summer and would love to take my family (kids 5 & 7) to an Italian town for a month. Large enough town that the kids could enroll in some camps, make some friends, and feel safe having some independence to walk around. My husband and I would find ways to live like locals and enjoy being present away from work. Any advice?
Research the weather. Much of Italy, including the area around Florence, is likely to be persistently hot during the summer. Other places not at altitude may be intermittently hot, which is a lot more bearable. Unless you stay way up in the mountains, I'd want air conditioning.
I'm a fan of Padua, but I expect you're looking for a smaller city. Padua's population is over 200,000. It offers lots of good side-trips by train, including Venice.
Two places I haven't been that sound very attractive are Treviso (less than half the size of Padua) and Merano (half the size of Treviso).
As acraven mentions, summer means heat. Most Italian families try to escape the city as much as possible in the summer with their children, heading to second houses or rentals near the sea or in the mountains.
Italian parishes organise GREST or summer clubs for children who don't go on holiday but they're usually just for local kids aged 6 to 14 and certainly wouldn't be in English.
Maybe campsites with bungalows for a fortnight each in two destinations on the sea but near to interesting places to visit. There's usually entertainment animazione/kids clubs and it would be a safe environment for them in contact with Italians and other nationalities.
Maybe somewhere on the coast in Marche region, lots of quiet villages to explore inland, Tuscany in the San Vincenzo area, or Puglia but latter could be very hot (Vieste area is beautiful ). Avoid August if you can. June would be ideal.