Palazzo Vecchio offers a wide variety of workshops and guided tours for children and families all year round. If your children are over 8 years old, take them to Palazzo Vecchio and join the Fresco Painting workshop. Kids will dabble in the different phases of making a small fresco, and they'll have the possibility to take their creation home with them at the end of the activity.
If your children are younger, from 4 to 7 years old, let them have fun with The Story of the Turtle and the Sail. After watching a video about the story of an old turtle that Cosimo I de Medici met (and saved!) when he was a child, they'll explore the floors, walls and ceilings of the Palazzo, in search of the symbol of Cosimo I: a turtle with a sail hunt.
Other family activities include a visit to the Secret Passages, a taste of Life at Court during the 16th century, and a Guided tour by Giorgio Vasari himself (well, sort of!). And we could go on and on, for more information, prices and booking check out the website of Mus.e Firenze.
Pro tip: the museum of Palazzo Vecchio also offers a special Family Kit, with several useful tools such as a map, binoculars, a photo album of the Medici family, crayons to draw and more.