Please note that because the garden is very steeply terraced and partially bordered by a lane, young children need to be supervised while playing.
But one of the reasons we bought a house in Italy was because holidaying with children is so easy and enjoyable here. Our children (aged fifteen, thirteen and eight) love it. We have found that restaurants are always welcoming and are happy to provide simpler meals. And there's always McDonald's in Lucca! There are plenty of trees to climb in the garden, and a play park in the public gardens here in Bagni, as in most towns. For outings, you could hire bicycles and ride around the city walls in Lucca, take a horse and carriage ride around the old centre of Florence, go to the beach at Viareggio, or go canoeing along the local rivers.
Older children could rent mountain bikes and explore the National Park of the Apuan Alps, visit the Grotta del Vento (an underground complex of caves with huge stalactites etc) near Barga, go swimming, sailing or windsurfing at Viareggio (above), or take a boat trip to the Cetacean Sanctuary (including the Tuscan Archipelago and Ligurian sea) to see dolphins and whales.