We spent two days in Lucerne in early March, and probably should have spent one more day because it was our first trip to Switzerland and because it was just so damn enjoyable. Arrived by train from Paris in the late afternoon, stayed at Hotel Walstaetterhof right across the street, and had easy access to the river Reuss, the Chapel Bridge and the Old Town. Spent the next day just walking around, having lunch at--believe it or not--the Manor Department store cafeteria, with rooftop dining (you carried your tray up there!) in which the vistas in every direction were spectacular. Phenomenal choice of food, reasonably-priced for Switzerland. Also visited a couple of boutique chocolatiers and the Lion Monument. We left via train for Italy the next morning, but had we had the extra day, a boat cruise and maybe a visit to the casino on the other side of Lake Lucerne would have been in order.
What struck me about Lucerne (and maybe all the Swiss people) is how nice & helpful they all were. Virtually all of them spoke perfect English, and were all like tour guides in trying to make our stay memorable. It was no more than 45 degrees & during the week (Tuesday), yet many locals were soaking up the late winter sun while dining al fresco at the numerous cafes or the Rathaus Brauerie--fantastic lager. I guess it must be nice to be neutral!
Here's the thing, though. During this trip, you really need to take a train through the Alps if you can do it. After leaving Lucerne, we took the south but eastern route, not toward Lauterbrunnen but toward Chiasso at the Swiss/Italo border. While it is not rated as anything unique, that path was still unbelievably scenic--at one point we rose up above the snow line into a squall, then down to Chiasso for the change, where it was 60 degrees. I can only imagine how the other routes are.
Enjoy!