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One of the great activities that you can enjoy while in Lucerne, Switzerland is cruise on Lake Lucerne and visit Mt. Rigi. You take the boat over to Weggis and go up the mountain to Rigi by cablecar. At the top you can walk around and enjoy the views, then take a rack railway back down to Vitznau, finally catching the next boat for a return journey back to Lucerne.
The other great mountain to visit near Lucerne is Pilatus, easily reached by boat and rail, and an enjoyable option to consider on your way to Pilatus is a stop at Bürgenstock. It's a small mountain plateau with a dramatic cliff-hugging walking trail. Most of the boats to Pilatus stop here en-route so hop off at the Bürgenstock dock, ride the funky old-fashioned funicular to the top and start hiking, following the signs to the cliff walk. This is a level path with sweeping views across the lake and at the rock face of the mountain, looking straight down about 1000 feet. You can have snacks or a meal at the restaurant other attractions on the plateau, which include more hiking trails through the forest, several newly-built deluxe hotels and a nine-hole golf course.
From Bürgenstock continue by boat and rack rail ride to the top of Mount Pilatus. You take the boat to Alpnachstad, one hour and 10 minutes, and then you ride up the world's steepest cogwheel railway to the top of Pilatus for sweeping view of the lake.
They do have a lovely rustic restaurant at the top and there's even a hotel up there that you could spend the night at. You can return back down the same way on the rack railway or for a slightly faster alternative with a totally different routing and some variety, take the cable car down the backside of the mountain to Lucerne.

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