If you want to go for a tour, I'd recommend calling or passing by the Zurich Tourism office, it's at the end of the hall in the main station, past the big "angel" hanging off the ceiling..
Any great galleries, hip happening areas, good markets etc... on your must do list?
Head to the Jules Verne bar in the evening and there is a day gone.
Walks, to get a view of the city and if it’s a sunny day, head down to Zurichhorn (by tram or car) and then walk along the lake side park to Belleview (it will take 30 mins approx) You get wonderful views of the lake and the city a s you walk up. With a few places to stop and get a drink. If it’s a weekend or evening you get to see a lot of the locals and sample a bit of Zurich atmosphere.
For culture, head town to the Kuntshaus www.kunsthaus.ch , its has all the big names, Picasso, Monet, Van Gough. Plus its free with a Zuri Card and about 10mins walk from Belleview
O f course the old town and Utilberg are worth looking up too.
Things in my view to avoid:
1) The landesmuseum (or Swiss National Musem) you can go and walk around the court yard for free, which is good. But inside I found it rather sterile and noting of significance (especially compared to the British Museum etc al)
2) Langstrasse (RLD) a lot of tourist books give the impression that’s it’s the edgy/ bohemian part of town and, but in reality if you are looking for that then you are in the wrong town and it just a bit dirty and grim. Useful place for a large pub crawl.
3) Buy gifts from the shiny shops in Bahnhofstrasse, most things are way cheaper in Migro/Coop and of the same quality, actually my family prefer the chocolates from Coop rather then the swanky stuff I used to get from spungli!