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Get a beautiful view over the Mittelland and its lakes on this 2-hour walk. Go there by boat (Lucerne-Kehrsiten) and funiculaire or by train and bus (Lucerne-Stansstad-Bürgenstock). There are some luxury resorts at Buergerstock. It's also possible to go by mountain bike to the top.
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Nice theater with a bar. A place for art work and to meet people. Inexpensive.
Verkehrshaus der Schweiz
With its large collection of trains, planes, automobiles, and motorcycles, this museum of means of transport is a great place to spend an afternoon. If you get tired of the real train engines you can check out the model railroad or the miniature working steam train. The air section also features several space travel exhibits, including an unused project Mercury capsule.
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).