Hello,
You'll love Luzern. Things to do include walk through Altstadt, including the two covered bridges and along the medieval ramparts; Lion monument, Bourbaki Panorama, Rosengart art museum and Transport Museum. Boat on Vierwaldstattersee (Lake Luzern) if they run in March and the weather is good. I'm guessing lots of clouds, rain and fog, so who knows if this will be an option.

I don't think you can get to the top of Pilatus then, but haven't checked in a while.

You haven't mentioned places to stay or eat. We like the Hotel Des Alpes'riverside rooms with balcony. Great view of Pilatus and lake. Their restaurant, as well as the Cafe Hug and Rotes Galler, are on the river. Good food, great views. For a splurge, the Old Swiss House has elegant service and gourmet-eligible meals.

Enjoy

When we were in Lucerne, in december 2003, Chateau Gutsch was closed. The funicular run, the courtyard was open, but the hotel and restaurant were closed. Do somebody know if it reopened?

I second JN's recommendation to eat at the Old Swiss House. They serve the best Wienerschnitzel anywhere, way better than in Wien/Vienna. They make it tableside right in front of you, then you'll learn how to make a good schnitzel. It's just a few blocks south of the Lion Monument.

Great! I really appreciate the ideas. I was afraid this wouldn't be much of a stop, but now I think it could be one of the best. Thanks, everyone.

Yes it's one of the best base cities and cities in general of its size in Europe - you can't go wrong. Just too bad you can't go several weeks later in better weather for climbing mountain tops and hopping lake boats.