Long stay in Italy June-July

Vicenza

It's hot in much of Italy at that time of year, so be sure your lodging place is air conditioned. That is not a given in some places in northern Italy.

Will any ol' airport do, or does it need to be a major one? There are airports (used by at least one budget airline) in Bergamo and Treviso, both attractive smaller cities. Bergamo's east of Milan; Treviso's north of Venice, which of course has a larger airport.

The Wikipedia entries for airports list destinations you can reach via direct flights.

I'm quite a fan of Padua, which is just minutes from Venice by train. Padua has a lot of sights and also excellent day-trip options by rail (Vicenza, Verona, Ferrara, Venice). [Edited to correct typo on "Ferrara".]

Verona has an airport, which puts Bolzano close to your airport-access rule (some trains 1-1/2 hours to downtown Verona; add time to get out to airport). Bolzano has rail links to Bressanone, Merano, and other interesting spots. There are buses going up into the Dolomites.

If you want a smaller place, look at Bassano del Grapa (less than 1-1/2 hours from Venice by train). I haven't been there but have read good things about it on the forum.

Padua is not exactly small but if you stay in the historic center it feels small. For actually small try Treviso or Parma.

I agree about Parma, not exactly laid back but as a town it's enough wealthy to seem laid back.

Bologna's Marconi Airport can be reached by train changing at Bologna Centrale station.

Lucca is an option. Pisa international airport is within an hour. What do you mean by easy access to youth/group activities? For yourself or your children? What type of activities?

FLORENCE
Near an airport (Distances from Florence city center: FLR= 15 min, PSA=70 min, BLQ= 90 min, FCO= 2.5 hrs). Also a major transportation hub to day trip to most of Tuscany
Not a major city (less than 400,000 pop in the city limits, 1.5 M metro area)
Easy access to youth activities (plenty to choose from, it's a major university town)
Away from busy tourist magnets (if you choose the right neighborhood)

The only drawback is the scorching temperatures in July and August, but that is true anywhere in Italy unless you stay way high on the Alps, or on the coast where there is some breeze.

If you like smaller and on the coast, I'd choose Sorrento or Venice.

June-July could be warm in Italy, so a place among the mountains should be better. the point is that the better places are more difficult to be reached...
If temperature isn't an issue any small Italian city could be a place to stay for you. Emilia-Romagna could be a starting point, mainly the cities on the Emilia road because are the ones on the main train line, so with easy access to any other place in Italy: Piacenza, Parma, Reggio Emilia, Modena, Forlì, Cesena, Imola. And why not Bologna itself? Isn't a town for sure, but when in July the most of university students leave the city it became a quite place: touristy but not too much, with plenty of activities both in city and in the countryside.

Imperia - on the Italian Riviera near the French border, close to both Genoa and Nice airports. Good-sized small city/large town, lots to do and won’t be as scorching as inland. Spent a week there in June this year and really enjoyed it. It seemed to have a lot going on in terms of locals coming and going, though it gets more touristy in the summer, mostly Italians headed to beaches. It has rail service, but not high-speed.

Thank you all for your detailed and thoughtful recommendations, especially about AC over that time of year and a proximity to transportation. I'm excited to research more about your recommendations over the weekend. Thank you!!