The last time I was there, there was something like a "metropass" you could buy for the weekend that let you on all public transportation and into all museums in the city. Seemed like a pretty good deal.
The bike path along the lake front through the Bellevue neighborhood was a pretty nice morning jog.
Once spent a couple of interesting hours sipping a beer, reading, and people-watching at a little sidewalk cafe at the lake-end of the Bahnstrasse. Every over-the-top sportscar I'd ever heard of went by. Children and mistresses of oil sheiks and drug lords, on their way to buy new rolexes, I imagined.
Also, if you want to get out of town for a few hours, there is an excellent system of bike paths. (Wanderwegs) that go everywhere. You can rent bicycles at any train station. (If you feel lazy, you can take a train to the upper end of a valley and ride back down.) I remember riding to Winterthur and back was a decent short ride. Once we spent a day riding to Rheinfelden, hitting a couple of castles and breweries on the way. Ended up having the most amazing four-course dinner (served with four wines) in a little restaurant overlooking the Rhine... all pitted out in damp smelly bike clothes.
Or course, you must go to a supermarket somewhere in the suburbs and load up a duffel bag with five or ten kilos of swiss chocolate. Back in the US, this stuff will get you laid.
edit: oops. prolly not "saturday night" activities. sorry.