Berlin and Hamburg are my favorite German cities, you could easily spend 8 days in both. Berlin is rich in museum (art, history mostly) and a very changing cityscape due to its history. There are lots of very different neighbourhood, restaurants and happenings. Hamburg has local foods, a different cityscape than everywhere else in Germany and lots of neighbourhoods. I was personally disappointed by Munich but think I should give it another chance. Cologne is very disappointing I think.
Bavaria has castles and nice villages that you could visit.
Travel within the country is easy. Trains are plentiful and the network extensive.