Lake Promenade: from Bellevue, just walk along the lake. There are always lots of people, artists, and musicians in the evening, especially during summer.
Old Town: Lindenhof, Fraumünster (with beautiful Chagall windows) and Grossmünster are definitely worth a visit! Or just walk through the old town and have a look at all the beautiful old buildings.
Bahnhofstrasse: this is where you find all the shops and banks (of course!)
Quick Tips:
Nightlife: There are a lot of bars and clubs in the centre of Zurich, but also check out "ZüriWest" (the area around the Escher-Wyss-Platz is full of cool places!) To go dancing, go the the Tony-Areal where you find several different clubs, to the "Kanzlei" (former gym-hall, close to Langstrasse), the "Palais X-Tra (free entry on Mondays, close to the Limmatplatz).Best Way To Get Around:
By public transport: buses, trams or trains. Don't even try to go by car, you will end up spending all your time looking for a parking space! Zurich has got one of the world's best public transport systems: punctual, reliable and so extended that you get everywhere by bus.