Berlin imo and Hamburg is also cool. Both Cities have flair. Münster and Heidelberg are pretty cool student cities.
Cant say a lot about Munich because ive been there only once, heard its kinda like the Miami of Germany in terms of people with plastic surgeries. But is apparently a beautiful city to live in, also expensive.
South germany is in general more beautiful than north germany (hills, drier and warmer weather, alps, black forest), that being said, the 2 coasts of north germany are looking better than everything the south has to offer.
But Bavaria and Baden Würtemberg are surely the most interesting places for tourists.
I would just avoid east or west-germany.
The east is poor, boring and right-winged (the big cities are fine though and very beautiful), and the west is too much industry and too crowded.