Its a difficult question to answer.
Firstly almost everywhere in Zurich is good for Swimming pools (lake) and schools. Zurich isn't great for big parks like London or New York, however there are a lot of children's play areas. To be honest I wouldn't worry about that.
However if you want an English speaking school then I think you have to be near Aldiswil (no kids someone will correct me if I am wrong)
However that's a good 20mins trek from the main train station by S-bahn...not bad if you work in Zurich but nasty if you have to go to Basel everyday.
Almost all areas of Zurich are safe, and have a lot of facilities for your family. certain areas like Enge and especially Seefeld (top of lake nr town) are where the rich want to live, you can get a 3/4 room apartment but it will cost you a lot more than it would in Kloten (airport)
Either side of the lake are where most people want to live with the right side (Meilen, Zollikon etc) being the most popular. Thalwil, Horgen on the other side of the lake are nice areas and because they are not in the centre of town, or as desirable are more affordable.
However again commuting to Basle or Zug will be more difficult.
The big factor will be though, how long do you have to look for an apartment, getting nice places at a reasonable price in Zurich is tough, and you may like an area but probably won't be able to find a place there, unless you have a good 3 months to look. ie there are not many apartments on the market, or more accurately there are but there are also a lot of people wanting them.
You will have more luck finding a place in an unpopular area like Uster or kloten than you will in Seefeld, in my opinion neither of those places are bad, they are just not on the lake or 5 mins walk to the Bahnhofstr.
Edit
http://map.search.ch/
seconding this link by Chemgoddess, will show you the facilities in an area.
Also look on this site for a big thread discussing the areas of Zurich proper.