The christmas market takes place every year in the city center and at the harbor of Constance. The locals like to meet each other on the christmas market for having a cup of mulled wine. Have a stroll over the market, buy some handcrafted gifts, get something to eat, enjoy the atmosphere and sipp on a hot drink.
If you would like to do something very German you should visit a Christmas market. Of course you can visit a Christmas market all over the world, but be sure that the food and the drinks in Germany are unique ( and pretty good too !)