Berlin is the capital and largest city of Germany. It´s recent political history has left its marks, for example with the remainders of the Wall that separated East from West. Nowadays it is a very vibrant international city with lots of young people, startups, fashion, restaurants and art.
Dresden is a nice city in former East-Germany. The royal buildings are among the most impressive buildings in Europe. The most prominent building in the city of Dresden is the Frauenkirche.
Hamburg is a major harbor and has nice sites and cafes. The old Speicherstadt and new Opera Building feature great architecture. Also worth visiting is the Miniature Wunderland, a very large, running model train that features many world sites. And yes, it's most famous, world-renowned citizen is the edible Hamburger!
Frankfurt am Main is a major city and hosts the largest airport of Germany. It is also a large financial centre and home to the European Bank.
München is the 3rd largest city of Germany and a highlight to any visit. It is great to have a beer here, during or outside the "Oktober fest". If you can get tickets, you may want to see Bayern Munich, one of the top clubs in Europe. The Black Forest is nearby for relaxing...