If you are in Zurich on a Saturday between the months of May through September, make sure to check out the vast antique & flea market on the Bürkliplatz in the city. It is a virtual cornucopia of treasures for the antique hunter. Be sure to bring plenty of francs along though; although bargaining is not unbeknownst to the Swiss, it is not as common as it is in the US nor is it the easiest to accomplish unless you speak the local dialect or German.
In the winter, Zurich features an elaborate yet quaint outdoor Christmas market that simply cannot be missed. Grab a cup of "gluehwein" (spiced wine) and warm yourself from the inside as you enjoy your outdoor shopping adventure.
Quick Tips:
If money is of no question, Zurich offers an endless number of things to do and see. However, if you are on a tighter budget, your best bet is to stick to the simpler pleasures the city has to offer.
Best Way To Get Around:
I highly recommend walking or driving through the city in order to get an idea of all Zurich has to offer. Although I felt perfectly comfortable wandering aimlessly through the city, this is not for everyone. Taxis are quite expensive so if it's public transportation that you prefer, Zurich features a reliable tram and train system that weaves throughout the city and as well into the towns and villages outside of the city.