If you want to meet locals with small children you can try either of these locations.
If you want to see a typical Zurich “Badi” (swimming area), walk along Lake Zurich through the “Arboretum”, then pass all the rowing and sailing clubs and the “Sukkulentenanlage”. After this nice walk, you can enjoy yourself at the small beach of Badi Mythenquai (bring along sandbox toys, waterproof trousers and rubber boots and, ideally, spare clothes for your little ones). There is also a small playground and a park. In summer it is fantastic to go swimming there and it has a very nice swimming pool for small children (< 30 cm of water).
Go to Bäckeranlage:
Stroll through “Kreis 4” and down “Langstrasse” and then finalize your walk through the city’s bar and red-light district by going to the park “Bäckeranlage”. It has a small playground and a small family-friendly restaurant with great soups and other daily specials.