I lived in Germany a couple years. There's lots of cities with phenomenal history. Depends on your interest. The above recommendations are good and have a lot to offer. Myself, I'd lean to Cologne (Koln) because it has has a Roman history, the Rhine and other elements. Cities in Germany, however, are a bit of a misnomer. They often just flow into each other. Think of visiting a region more so than a 'city'.