I´m sure you want to discover your host country! Be curious, Germany has lots of nice destinations to offer. Landscape, dialect and mentality differ between north and south, east and west. Also the typical dishes.
I am sure you will have great experiences if you engage with the German culture.
timbered houses in Bretten, Baden-Wuerttemberg
population: 3.5 m inhabitants
best time to visit: May to September, when you can walk around or sit outside without freezing!
population: 1 m inhabitants
famous for: Kölner Dom, Kölsche Brauhäuser, Kölner Karneval, Eau de Cologne, 1. FC Köln (I needed to place this here because my husband is the biggest fan on earth of this soccer club ;-) ), Hohenzollernbrücke. It is the most populous city in North Rhine-Westphalia and people here are very open minded.
best time to visit: in February for Carnival, otherwise during the warm month to enjoy a boat ride on the River Rhine, climb up the 500 steps of the Cathedral tower or have a Kölsch (beer) in a "Biergarten".
where: North Germany
population: 1.8 m inhabitants
famous for: Reeperbahn, St. Pauli-Landungsbrücken, Michel, Altonaer Fischmarkt, Elbphilharmonie, Speicherstadt. The weather is famous for being bad ("Hamburger Schietwetter"), but I cannot confirm this as mostly when I travelled to this city the weather was pretty good.
best time to visit: in December for the Christmas markets, otherwise from May to September to enjoy the Harbor Promenade and cruise the canals.
where: South Germany
population: 1.4 m inhabitants
famous for: Oktoberfest, Englischer Garten, Marienplatz, Hofbräuhaus, Viktualienmarkt, Olympiastadion, Frauenkirche. München is the capital of Bavaria. Bavarians speak a very strong dialect, so don´t despair if in spite of speaking German perfectly, you hardly understand a word. ;-)
best time to visit: March to May is less crowded and not so rainy, but if you like to party, the Oktoberfest at the end of September is the best time.
where: South Bavaria
population: nobody, but it is visited by around 1.5 m tourists per year
famous for: I think this is the most photographed castle in Germany. Walt Disney chose this fairy tale castle as a template for his films.
best time to visit: purchase your ticket in advance or arrive one hour before opening time. The quieter months are from November to April. This is a very popular castle in summer!
population: 1500 inhabitants in St. Goarshausen
famous for: The Rhine is Germany´s most famous river. Legend has it that the water nymph Lorelei lured boatmen to crash against the rock with her beautiful songs. The Lorelei rock is close to St Goarshausen, with its beautiful Castle Katz.
best time to visit: day cruises along the River Rhine are available from about May to September
famous for: Germany´s most well-known island in the Baltic Sea. The white cliffs are unforgettable!
best time to visit: May to September
where: Spreewald, 100 km south of Berlin
population: 50,000, descendants of Slavic Sorbs or Wends
famous for: Go punting and enjoy the over 200 small canals in the Spreewald.
best time to visit: the summer is warm but rainy; most tourists prefer to go from August to November
where: Black Forest (Ger. "Schwarzwald"), in the southern German state of Baden-Württemberg
famous for: one of the most well-known regions in Germany, especially for its hiking trails and mountain bike routes for the summer and skiing facilities for the winter. Cuckoo clocks are available all year round!
best time to visit: hike in the summer. May, August and September are the most popular months. Enjoy winter sports from December to February (depending on the amount of snow!)
where: Zugspitze is in the Alps, in Bavaria, on the frontier with Austria
inhabitants: Bavaria has nearly 13 million inhabitants (but they don´t live on the Zugspitze!)
famous for: it is the highest mountain in Germany (2,962 m). The Alps are the largest and highest mountain range in Europe. Incredible glaciers, skiing and views!
best time to visit: on a clear day in summer