I arrive in Zurich on Dec 2nd at 11 AM. I need to be in Zurich from Dec 6 - 8 (a weekend). I would like to go to Lucerne for one day and skiing for two days (one night). Any other suggestions at to which other places I should visit? Can someone recommend a logical plan for a trip during the winter. Not all ski resorts are open at this time. I will be traveling with my husband and 18 year old daughter who loves museums and just about anything. I would love to include a scenic train ride to one of the places we visit.
I will not be renting a car and would like to take the train to all destinations.
It's a good choice to travel by train since the railway system in Switzerland is completely reliable and perfectly cover all destinations (even the most remote places up on the mountains). The only downside: it is quite expensive (but so would be to rent a car in Zurich).
You can find all the information you need about train-travel in CH here.
Luzern is a typical swiss city that is worth a visit. The area surrounding Luzern is extremely beautiful (4-Cantons Lake) but you're not in the Alps region yet (here the mountains are between 1000 and 2500m). If you want to be closer to higher summits and true alpine scenery i recommend you to go to the Bernese Oberland (Interlaken/Lauterbrunnen/Grindelwald). It's only 1h30 from Zurich and it's very well developed for tourism (more info here). Ski-resorts can be found here and you have the highest-altitude railway platform in Europe (Jungfraujoch trainJ
Visiting both Luzern and the Oberland is completely possible in 3 or 4 days if you want to enjoy those places and some activities. But remember Switzerland is one of the most expensive countries in the world!
Good luck and happy travel!