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Lucerne has an excellent bicycle Network. Rent a bicycle at the train station in lucerne and explore the city and the suburbs or make a day trip on the national bicycle network (http://www.veloland.ch/en/veloland.html).
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Take a boat tour on the lake Lucerne with the traditional steamboats. A ride along the full length of the lake (Lucerne – Flüelen) takes approximately 3 hours. The lake has several tight bends and the landscape changes dramatically during the ride from the high mountains around Flüelen to the gentler hills around Lucerne. The villages and towns along the lake are generally very nice places to take a relaxed day with a walk/swim and food at the lakefront - Weggis and Brunnen for example. Flüelen and Brunnen at the far end of the lake can also be reached by direct train from Lucerne.
Kunstmuseum Luzern
Kultur- und Kongresszentrum Luzern
The KKL is a spectacular building that contains several concert halls and the Lucerne Art Museum. It was designed by Jean Nouvel. Its major concert hall ("La salle blanche") is famous for its acoustics, and world class orchestras can be heard regularly. It hosts the Lucerne Festival (classical music).
Sammlung Rosengart
Well over 200 works by 23 artists of early modernism, including 125 works of Paul Klee and about 50 by Pablo Picasso. Also works by Cézanne, Chagall, Miró, Pissarro, among others. The collection also houses 200 photographs, previously housed in the Am-Rhyn-Haus, by David Duncan Douglas, Life Magazine’s World War II photo correspondent who arrived with his camera uninvited at Picasso’s villa “California”, was welcomed by Picasso and his family, and over the years produced an intimate portrait of the artist’s day-to-day life. Picasso's living room was his studio, and domestic scenes — a ballet lesson, Picasso drawing with his children, or wrapping himself in the cape and hat of his native Spain —play out within the backdrop of some of his most famous works. Allow at least 2 1/2-3 hours to see all the artworks. There are three floors, and you should allow plenty of time for each one. The ground floor houses many very interesting works by Picasso, but there are lots of others on the first floor, along with outstanding works by Raoul Dufy, Fernand Léger, Vassily Kandinsky, Georges Rouault, et al. The Klees are all in the basement. The titles in Klee's handwriting are often very small and hard to read, and he did not put titles in every work, so ask for a printed list of composition titles for them.
Kapellbrücke
The Chapel Bridge was built in the 14th century to aid in the protection of the city. It is a landmark of Lucerne and is said to be the oldest wooden bridge in all of Europe. A point of interest as you walk over it are the paintings in the rafters depicting 12th-century city life and Swiss history. The bridge was badly damaged by a fire on 18 August 1993; it was rebuilt within a year, but the damage is still visible in places and many of the original paintings were lost. The tower which has had multiple uses over the years (including as a dungeon) is still in the original condition, but not open for visitors.
Top end theater and musicals