Lucerne is built for excursions. The lake's boats and a dense network of mountain railways put a whole region of peaks, valleys, and lakeside towns within an easy day's reach of the old town.
The obvious trip is Rigi, the mountain massif rising straight out of the lake to the east. Take a boat across to Vitznau and ride Europe's oldest rack railway to the summit ridge for one of the great central-Swiss panoramas, then come down a different way to make a loop of the whole mountain. Mount Titlis, reached by train to Engelberg and a sequence of cable cars onto a glacier, is the other big mountain day — snow and altitude without any technical effort.
Closer to hand, the Felsenweg on the Bürgenstock is a short cliffside walk above the water with wide views over the lake and the surrounding peaks. The lake boats themselves are worth a day, calling at Brunnen and Flüelen and at the meadow of Rütli, the mythic spot where Switzerland was said to have been founded.