Regarding stops between the two cities. You can take the direct route, a northern detour via the Harz mountains, or a southeastern detour via Dresden.
Direct route
On this route you cross the cultural heart of Germany, with many World Heritage Sites (WHS). Basicall a "Best of Germany" tour, which works best with a car. Here is a list from north to south:
Wittenberg (WHS) - preserved, small town, home of the Protestant Reformation (Luthers + Melanchthons house)
Dessau-Wörlitz Garden Kingdom (WHS) - one of the first English parks on the continent
Dessau - Bauhaus sites (WHS)
Leipzig - trading city with a nice 19th century centre, Bach, Mendelssohn Bartholdy, great zoo
Naumburg - preserved town with a famous Gothic cathedral (WHS)
Weimar (WHS) - preserved town with castles and parks, Goethe, Schiller, Nietzsche, Liszt, the Bauhaus, Weimar Classicism
Erfurt - one of Germanys biggest preserved town centres
Wartburg (WHS) near Eisenach - Germanys historically most important castle
Coburg - preserved old town with a massive castle
Bamberg (WHS) - beautiful old town with a famous cathedral
Nuremberg - Nazis tuff
Regensburg (WHS) - biggest medieval old town of Germany
Northern detour
This is a great idea if you want a change between the two big cities. The Harz mountains offer several small towns with literally thousands of half-timbered houses. Two of them, Goslar and Quedlinburg, are World Heritage Sites, but Wernigerode, Stolberg, or Wolfenbüttel are just as good. The region also offers the biggest steam train network of the country, and from Wernigerode you can take the train up to the Brocken, the highest peak of Northern Germany.
Southern detour
This "Best of Saxony" detour offers a bit of everything. Stay in Dresden, which offers world-class museums, which are quite unique (among them the Green Vaults and a great armoury). The suburbs of Dresden are former wine villages with vineyards, castles, palaces and posh villas. In the surroundings are beautiful preserved towns like Meissen (porcelain and huge castle), Bautzen (Baroque town surrounded by medieval fortifications) or Görlitz (best preserved town of Germany). A fleet of nostalgic paddle steamers brings you to sites along the Elbe, like Pillnitz castle, Meissen, or Königstein fortress. And the nearby Elbe Sandstone Mountains (also called Saxon/Bohemian Switzerland, try a Google Image search) are perfect for hiking.