If you're having an night out in Zurich, the best place to head (like for everything else) is the old town, where most of the bars and clubs are situated.
Zurich's nightlife revolves mainly around café bars, where you can start the evening off with a meal before heading to the bar for drinks, and amongst the best known are Kaufleuten, Café Bar Odeon, and the Jules Verne Panorama Bar, which has great views over the city.
Nightclubs tend not to have dress codes, and are fairly relaxed. The most modern of them are located around the Main station in the west of the city, and Rohstofflager is a popular choice that attracts a mixed crowd, while Dynamo is a new and very fashionable place to go.