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.
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.
The train from Innsbruck to Munich takes less than two hours.
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.