On Saturday mornings from 6am to noon this bridge hosts a market where residents come to buy mostly vegetables, but also flowers, bread and some fine food delicacies. It's surrounded by cafés, so after you've done your shopping you can stay to do some people watching, too.
Even if you don't need groceries this bridge presents the best location in Zurich to be right in the midst of old town both with a view of the Limmat river as well as the Lake Zurich. The square has been a market since the early 14th century and is adjacent to the city hall, resulting in its official name "Rathausbrücke".