Yes, we have Giardino di Boboli, which is beautiful (and has free entrance for residents), but which isn't the most child friendly place, since there are no playgrounds and everything is a bit museum-like. Also it is quite far from where we live, so it hasn't really been an option to go there with the baby.
But some weeks ago I heard someone mention a park near Piazza della Libertà, which should be quite nice. I knew absolutely nothing about it, but since it was just a small walk from where we live, I decided to check it out.
The park is surrounded by beautiful houses, it's completely closed, except for the entrances of course, so it's a safe place to bring children. It has a great playground, a lovely outdoor cafe where you can even have lunch, and the most beautiful gigantic Tepidarium (greenhouse).
We hung around for about an hour, Matilde enjoying the swings, I taking photographs and finally sharing a smoothie at the cafe.
This place is nothing less than magic.
Via Bolognese 17.