The Christmas markets are spread out around the Altstadt (old town), but most are connected by the pedestrian zone and the ones that are not can be reached by public transport. The highlight of Köln is the Dom (cathedral), the largest in Germany. For a few euros, you can climb one of the towers.
Quick Tips:
See www.koeln.de, www.duesseldorf.de, and www.aachen.de.Best Way To Get Around:
In my opinion, the best ways to get around any German city are by walking or taking the bus, tram, or subway. These are cheap and efficient, and except for the underground portion, a great way to see the town. At the center of most old towns, cars are out of the question due to small streets and limited parking. Take the train to Aachen to see the Dom and Rathaus.