Hello there!
I live in Wiedikon in a Complex called "Zurich Binz" which is super family oriented (there are Krippes and Kindergarten on the ground floor, playing areas and so on).
We are 2 minutes from the Zurich Binz train station, 5 minutes to main station. We also have 4 trams in walking distance 5, 13, 9 and 14.
In the nearby area (all walking distance) you have all that you are looking for (grocery stores, pharmacies, some restaurants, big shopping centres, pediatricians, etc etc)
It is not as glam as some of the other area (but upside is that is it also not as expensive

)
Postal codes for Wiedikon are 8045 and 8055.
Ciao
K