Although small, Zadar’s Archaeological Museum has plenty to offer a traveller with an hour to fill.
I’d definitely recommend a visit to the Bach Museum if you’re in Leipzig, especially if you’re a fan of his music. If you’re not, you might be by the time you leave!
Dresden is a city of art, and if you want to get your fix, the Altstadt in general and the Royal Palace in particular are the places to be.
If you’re interested in porcelain, then by all means visit the Porcelain Collection; otherwise I’d give it a miss.
Of the many museums in Dresden, one was recommended to us more than once: the Mathematisch-Physikalischer Salon in the Zwinger complex of the old town.
When in Cologne, a visit to the cathedral is a must, but a stop at the Kolumba religious art museum is also highly recommended.
A visit to the Nazi Documentation Centre is almost compulsory. The moving exhibit is housed in the Nazi Congress Hall on the Party Rally Grounds.
Be overwhelmed at the Germanisches Nationalmuseum (German national history museum). Rich collections, original masterworks by Dürer or Rembrandt and more.
The Museum König is a good place to spend a rainy afternoon in Bonn.
If you’re interested in Ancient Egypt and have a Bonn Welcome Card, an hour or so at the Egyptian Museum of Bonn University might be a good option.