Just got back from 3 weeks in Florence, Tuscany and Rome. Thanks for the gelati tips I received here--we went twice a day for gelati, as it's my daughter's favorite thing.
In Florence, Gelateria Badiani is the best, by far, but Neri, Carozze and Carabe were all extremely good (worth at least two trips each). Vivoli's was good, but living on its reputation a little. We thought Perche No and Festival del Gelato weren't worth the calories, and didn't go back.
In Rome, San Crispino, near the Trevi Fountain, was fantastic--their honey flavor is to die for. Giolitti was still pretty good as well, but not in the same league as SC.
As you know, most of the restaurants were closed, but we had very good meals in Florence at ZaZa, Trattoria Antellasi, Osteria Santa Spirito, and a great Birreria (who would have expected great beer in Florence?) right at the San Frediano gate, full of locals, with great non-traditional food as well.
In Rome, we liked Il Fico, near Piazza Navona, and La Duca in Trastevere had the best lasagne I've ever had.
Happy to provide more details if interested, and thanks for the suggestions from this board.