My experiences in Venice and Florence are years old now.
Venice was hard to navigate; I recall being unable to even find certain restaurants, never mind get into them. Without looking at my notes, the only meal I recall fondly was dinner at a family-run trattoria named Vini da Gigio. Yes, as their name suggests, they have a good cellar list. I remember an excellent risotto with goose and grated licorice root.
We found Florence even more difficult to deal with. Firstly, everywhere we wanted to go required reservations, which we tourists were not comfortable committing to. But if you show up at 7:00 or so, the restaurant is empty and the owner will turn you away -- it's all reserved and they don't turn tables. Yours for the night.
This was infuriating until we learned about La Passeggiata. This is a tradition of walking around town, with no particular destination in mind, simply to see and be seen and chat with your homies. It runs from 'after work' until 8:00, sharp.
I wonder whether you will still see these behaviors when you go.
One more thing: the food is always better if you eat what is seasonally available. (Which is likely to be all you will find, anyway, but a word to the wise....) In June, you might be done with asparagus and artichoke but you should have zucchini blossom, early melons, and maybe figs and citrus.
And it's Florence so there will be bread.
