I don't have any restaurant recommendations, but a couple of cafes worth a mention:
it doesn't have a play area, but in the Niederdorf we like Cafe Henrici
- they've always been very tolerant of us when we've been there and have a bookshelf inside with some kids books, crayons and a few toys on. We've also always enjoyed the friendly service (and the Flammkuchen!) there, not a given in Zurich!
There's also "Kafi für Dich
" in Kreis 4 next to the Bäckeranlage - though they've been a bit snarly about bringing buggies in to the place when I've been there (don't know what they expect if they encourage families with kids!) and it's hardly been service with a smile, there is a reasonably sized play area at the back with some toys, and a massive chalk board all across one wall. And if the kids get really tetchy there's the big Bäckeranlage
park across the road to let off some steam.