I would like to suggest the following options:
1. The OLD TOWN, Roam around on the streets of old town have dinner at one of the restaurants. Since it is Christmas time as well, its absolutely beautiful these days.
2. Zurich Zoo: The major attraction is the Penguin Parade when the Penguins will actually walk with you.
3. Grossmunster Church: This is a very beautiful church with incredible view over Zurich. Yes, for a small fee you can go to the top.
4. Uetliberg: The highest point in Zurich. If you are lucky then you can find some snow as well.
5. Bahnofstrasse: The place for shopping with widest options, its expensive though. Probably there will be some discounts on offer at the stores by the time you arrive.
6. Zurich Lake: You can also take a boat ride.
Take a 20 min train to winterthur and visit the fantastic Christmas lights (traditional.) and markets in the car free main street. It's beautiful, and all in one easy to walk town.