Late June/early July, with my family (including an 11- and 14-year-old). Staying one or more nights: Rome Venice Bologna Florence Milan Brescia Day trips to: Pisa Lucca Siena Ravenna What places do you recommend most highly?
I would suggest you get in touch with @Jack_14 - my trip was primarily to track down relatives with little sightseeing. Looking forward to your beer adventures!
One of the best beer bars anywhere in Europe is in Rome's Trastevere neighborhood - Ma Che Siete Venuti A Fà. There are tons of restaurants nearby as well. Rome will be extra-touristy this summer due to 2025 being a jubilee year, so...if this is a self-planned trip, I'd very strongly recommend booking anything you want to do as far in advance as possible (*especially* if you want to visit either the Vatican or the Colosseum).
Rome-Ma Che Siete Venuti A Fa Milan-Lambiczoon & Good Beer Drinking Venice-Il Santo Bevitore & Pub da Aldo
Since You will be in Brescia then it would be a crime not to visit lake Garda, and towns like Limone or Salo (bad history with that one, but very pretty). There is a Birrificio Manerba very close to those locations.