You may want to go through this thread on
where to live in Zurich City (if you haven't already) , you will find lots of opinions on what members here think about the various neighbourhoods - with or without children.
For what it's worth, we live in Kreis 7, near Kreuzplatz and are very happy with the local school(s). But there's always someone at one of the parents' evenings who has something to moan about. I'm sure that's the case all over, so it's difficult to just recommend a school to you...
There are a lot of English-speaking families in Kreis 7 and 8, but accommodation is hard and/or expensive to come by. I have friends (also English-speaking) in Witikon who are happy with their school - and there's a great adventure playground there. I've heard that the infrastructure (daycare and such) is very good for families in Kreis 6 (near university).
Other than that, I can only offer the advice to look for parks and playgrounds, and look for an easy way to school - so that the children can walk by themselves to school and back home again (and I don't mean the 4-year old, here

)