Nürnberg (or Nuremberg in English) has the most famous Christmas market, and that in Munich is not bad either, but any German city/town with a population of over 300,000 will have a significant Christmas market. The more 'traditional-looking' ones are in the south. An exception is in Frankfurt, which generally has a pretty poor show I find. Try Augsburg, Ulm, Freiburg, etc.

The entry to the Swiss Alps can really be anywhere, not necessarily Lucerne. Depending on how late in the year you leave it, you may wish to rent a car and drive through one of the mountain passes (closed in winter with snowfall).