Once you're back, the downtown area of Lucerne has many shops and nice restaurants, it's really nice there. I'd say stay at least 2 nights, with an option for a 3rd.
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Depending on your time budget, you could go from here to Innsbruck in Austria (and to Munich from there), or go straight to Munich. If you decide to make a stop in Innsbruck, the train takes about 5 hours. A reasonable hotel is the "Goldener Adler" right downtown. If you're lucky, you may get the "Goethe" suite, a room where german playwright J.W. Goethe stayed on a trip before. Just enjoy the medieval downtown and the hearty Austrian cuisine here.
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The train from Innsbruck to Munich takes less than two hours.
[[File:innsbruck-munich.png|400px|right]]<br clear=both>
[[File:lucerne-munich.png|400px|right]]
If you decided to bypass Innsbruck and go straight to Munich, the train ride from Lucerne via Zurich to Munich takes about 6 hours.
Munich and the surrounding area is next.