Kid friendly restaurants are normally many of the larger restaurants or even some smaller family run places. Pangies Bistrot serve portions for the kiddies. Also with desserts with plenty to tickle the palate of little child. There is nothing like being at Pangies since it is just like being at their home as their guest. Lorenzaccio is another great place to bring the kids. The waitstaff is always happy to see a child at their place. Giuseppe loves to talk with kids. There are child size portions as well, and if your kids like a simple sauce for their pasta, they will accommodate to you.
Kids are able to fit in just about anywhere in Florence. From a fabulous family run place like Osteria (Vini e Vecchi Sapori) where there only 17 people allowed in at a time to a large trattoria near Mercato San Lorenzo like Trattoria Zà-Zà which accommodate to many more. Being a culture that is surrounded by family and children running to and fro, Florence doesn't have any particular rules against children in restaurants. These top ten are probably the ones I would take the kiddies to on your first trip. The more romantic ones are the ones you will for sure pick out right away and which are not places that won't be to happy about having a 5 year old at the table. Trust your judgement on which places are suitable and enjoy the experience your children will never forget.
Via del Parione 43/45/R
Family-run restaurant with quality service and conversation...
Piazza della Signoria 32
Dine in style, looking onto Piazza della Signoria...
Via del Proconsolo, 39r
A quick bite to eat after a museum visit...
Via del Proconsolo, 8-10r
They are equipped with internet in the restaurant, so if you want to use your iPhone, feel free...
Via Pisana 3r(Porta San Frediano)
Florence's first microbrewery with restaurant...
Piazza Santo Spirito 6r
Pizza that will make your belly full...
Via dei Magazzini 3r
The alley off Piazza della Signoria to the left of the Palazzo Vecchio
A small venue with only 17 tables...
borgo La Croce 85
Great for Families, Tourists & Groups...
Piazza Mercato Centrale 26r
Via Palazzuolo, 100
A fixed price with great quality and family goodness...