Texan Guy, Kuiji75 provided the link about
Depend on your interesting and comfortable...
Great ! I would like to spend a week at least. 
Culture, museum, relax, hiking, wander, ???
Yep, you got it all right. I would love to learn their culture, musuem, historic, and of course, wanderin'. For my leisure time. 
Maybe, you can show me around some day... hmm ? 
As I know you love Alaska from your previous posts then I know Island of Sylt is best place for you and also old towns as well and romantic houses etc... There're plenty of fishes etc...it will remind you of Alaska.
My view of best cities, I visit to is:
Neuschwanstein, Linderhof castle, River Rhine, Rothenburg o. Tauber, Island of Sylt, Rüdesheim am Rhein, Mosel River, Trier to Koblenz, Königsee, Berchtesgaden, Mainz and more cities...
(I will be back if I remember...)
Ok.
I would suggest you to check those link which place you like to visit... and feel right for you...
Dresden 1999 Photo Gallery by Ralf Brown at pbase.com
I just bookmarked it and will look up tonight after helpin' with a friend of mine to remodel in a master room.
Most around Germany are old and romantic towns/cities....