What do you recommend seeing in the ZH area? I haven't had a chance to get outside of the city and visit the mountains, lakes...
Is there anything close and interesting? I was told Zurichberg is decent...

I think Uetliberg is a nicer trip than Zurichberg. You can find details about Uetliberg and many other suggestions in these threads:

Suggestions for hiking with kids?
http://www.englishforum.ch/travel-da...ctivities.html
http://www.englishforum.ch/other-gen...rich-area.html
http://www.englishforum.ch/travel-da...-days-out.html
Getting out of Zurich for Street Parade

Here are some interesting threads which have some info on what to do in and around Zurich:

http://www.englishforum.ch/travel-da...-days-out.html

Day trip from Zurich for "Swissness"

It may have been mentioned before, but I think Schaffhausen followed by a walk along the Rhine to the Rhine Falls is a good day trip.

You could go to Seilbahn Rigblick, go up on the cable car, walk up the hill and then along towards the lake until you get to the Zoo and then visit the Zoo. I have done the walk, but not the zoo.

I've been saving Winterthur for a rainy day, since I think the old town is supposed to be quite pleasant and there are loads of museums/galleries there.

Hope this helps.

kfc.

Suppose it depends on what you mean by close, an hour and 10 mins by train and you can be on Vierwaldstattersee where you can easily spend a day visiting various towns around the south end of the lake. Can be a bit touristy but my kids loved the William Tell Museum in Burglen and the trip on the lake to Rutli and Tell's Kepelle.

Schaffhausen as mentioned is a pleasant town and a walk by the river and on to the Rheinfalls is lovely as long as the weather is kind. Some of the local vinyards are worth a visit (I would recommend Fam Strasser at Uhwiesen, and only 10 mins from Rheinfalls followed by a nice meal at Gasthaus Hirschen).