Finding the right neighborhood (Turin)

Hello everybody. I am new in this group and still try to figure out how this works :D
Here is a question for you beautiful Torino people: My husband, our five month old baby, 2 dogs and me are planning to move to Torino. We live in Bolzano right now because of my husbands family. But I was born in the flat lands and turns out- living in the mountains is just not working for me. Torino looks about a good compromise for all our needs. Here is the thing- wich neighborhoods are good to live in? We're both mid 30ies and have a new born. I need long walks in the green every day, that I can reach by walking. Also for our daughter we wanna have a more quiet and kid-friendly neighborhood. Still it shouldn't be too far from the spot. We both enjoy a social life.
Is there places in Torino that fit my description or come close at least? I am excited for your answers!