This park is great with a nature trail and a few other trails for your little one.
Plus a huge grassy area for running around and getting out some of their energy.
There are wonderful children wooden carved playing sets
The name is Il Boschetto with many entrances to get into the park. The park entrance changes with the seasons, but opens all the time at 8 am and right now in winter months closes at 5pm Other times during the different seasons look here: hours
You can get in at Via di Soffiano
Via Pisana Polimoda entrance
Via Monte Oliveto
(this is way at the top and is very steep hill so use another one if you have a stroller )
Related Articles on the Park:
Il Boschetto – ioamofirenze.it
Teatro estivo Il Boschetto – it.wikipedia.org
Il Boschetto ( Firenze) – manets.altervista.org
Il Boschetto – yelp.it