Some good day trips or activities from Zürich:
Go to Winterthur by train (every 10 minutes or so, plenty to choose from including the S8, S7, and S12) and visit a discovery centre called Technorama. Here ths kids can learn all sorts of neat scientific things in a very hands on place.
Take a train to Effretikon (S3 or S8) and then the bus to Kyburg. Here is a castle that you can go through for about 3usd. It is quite fun to look around these (plenty of castles in Switzerland).
If you want to get a great view over the city, take a train to Uetliberg (the Zürich house mountain) and eat some fries and Bratwurst at the outdoor cafe of the hotel there.
For a fun water theme park day, take a train to Alpemare at the southern end of Lake Zürich, in Pfaffikon. This is very fun place for kids with lots of slides and so on, and the parents can relax in theraputic hot pools.
The zoo is fantastic, said above, and should be reached in a Zürich tram, another must do.
For a mountain trip from Zürich, I recommend taking the train to Luzern (every hour - one hour trip) and going up Pilatus (a mountain) by gondola. Return down the mountain on the worlds steepest cog railway. It is a little scarey, but normally more for us old folk.
Switzerland is incredible. I call it home.