Depending on when you arrive, you may want to see the cathedral on your first day. If you don't have the energy for this on arrival day, save it for day 3, and instead enjoy a leisurely walk around the Old City (Altstadt), join a free walking tour in German or English, or try a glass of Kolsch (the local beer) on the riverside. 

Aachen is nestled right on the border between Germany, Belgium, and the Netherland. Due to its proximity to hot springs, it's been a spa town since ancient times. Like Cologne, the city has ancient roots, and it became the capital of the Carolingian dynasty during the reign of Charlemagne. It was the coronation site of the Holy Roman Emperors for centuries, and many famous figures are buried there (including Charlemagne, though his tomb has been lost). The city retains much of its medieval charm. Even for non-history lovers, it's a wonderful place to spend the day. 

Today is your chance to see everything Cologne has on offer! Below are listed several options for museums and churches in the Altstadt area, and there are plenty of other things to see and explore while in Cologne. The city is populated with small neighborhoods called Veedels, each with its own character and local shops and bars. Examples include AgnesViertel, Ehrenfeld, Nippes, Südstadt. Please note that some shops will be closed on Sundays. There are also many options for relaxing boat tours on the Rhine, beer tours, and shopping areas. I would certainly recommend trying at least one local Kolsch if you like beer!