Hi Welcome,
i live in Wallisellen
i do not have kids,but there is Park to go
one little one is in SantiStrasse ,also
if you need like a day care ,there is one at the Glatt centrum
i see many familly with kids of all ages ,so you are in a friendly city for
familly wich is nice,about 3 weeks ago there was at the city hall parking a little fair.
Maybe go at the city hall of Wallisellen the gemeinde Haus,you can take bus 771 and stop at the Gemine Hause bus stop.
Have a good week end