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...
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.
Cologne (Köln) is mainly known for: the Dom (huge cathedral), the Eau de Cologne ("parfume"), Carnival and the location near the river Rhine. Locals may also add the beer and the football club...
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.
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.
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.