When Charlemagne was crowned emperor, Aachen became the capital of the Holy Roman Empire. Although the town soon lost that title, Aachen remained an important destination for pilgrims because of the valuable relics brought there by Charlemagne. In the centre of the old town is the Pfalz, a complex of buildings belonging to Charlemagne's former palace. They include a cathedral with a palace chapel and a hall which was rebuilt as the Rathaus.
The old centre of Aachen is relatively small, with the Pfalz being the main point of interest. There are however lots of shops and places to eat, so rather than being somewhere to stay, Aachen is a great place to stop off enroute to another destination.
Aachen really comes to life at the end of November, when the Christmas Market opens. For me this is the best time to go there, you can visit the Cathedral whilst sampling the unique atmosphere of a German Christmas Market. People travel from far and wide to visit Aachen at this time of year, so it can get very busy as the day progresses.
Try and get there when it opens around 11am to avoid the crowds which build up in the afternoon. It's worth staying till it gets dark, as the market really comes alive when you get the true effect of all the Christmas lights. If you enjoy Christmas markets, take a look at our blogpost on Cologne.