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.
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...
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!
Heidelberg is a 800 year old university city on the Neckar river. It is a beloved touristic location thanks to its cityscape. One of the biggest tourist attractions is the Christmas market during the winter time.
Aachen is a nice city, with a cosy old town, at the border with The Netherlands and Belgium. It is home to the 1200 year old Dom/Cathedral (#1 on UNESCO heritage list, since 1978).
The Chiemsee (aka. the Bavarian Sea because of its size) is a lake in the province of Bayern.
Garmisch-Partenkirchen is an Alpine city on the border with Austria. The Zugspitze (highest mountain in Germany) is nearby. The city is known for great skiing including famous ski-jumping tournaments.