Aachen is very close to Köln. I don't think there is anything worth to stop between the 2 cities. I think you can spend a whole day in Aachen, especially in November when the sun sets around 4-5pm.

Düren is the main town between Köln and Aachen, but it was totally destroyed by Allied bombing in WWII.

Stolberg is not directly between the 2 cities, but very close to Aachen with direct trains taking only 10 minutes and it has direct trains to Köln as well. It has a nice castle and a little old town.

https://de.wikipedia.org/wiki/Burg_Stolberg

https://www.stolberg-erleben.de/sehenswert-uebersicht/

If you walk fast and want to see only the highlights of Aachen in a couple of hours, than you could combine it with a trip to Maastricht(hourly trains, the trip takes 1 hour), but it may be too much for a short winter day.

If you choose the Maastricht option make sure you have your passport with you as you will cross into the Netherlands, where photo ID is required at all times. Also passport checks on trains are not unheard of.

This is one of the most heavily destroyed areas in WWII with Jülich and Düren being the record holders for destruction levels among towns. The day will be short anyway, you'll want to see the treasury and catch an English tour of the cathedral (or else you don't get on the upper gallery), also see the town hall. If you don't want to fill the day up with museums like the Couven or the Suermondt-Ludwig then you could consider a short trip to Kornelimünster by bus. It is today a part of Aachen but a nice historic town with a significant main church.

There's not a lot to see in Stolberg. Really not worth a stop. Spend the day in Aachen.

Aachen will need your whole day. Enjoy!
Sounds like you will not have a car, but if you do, or want a tip for another great Christmas market, 20 miles south of Aachen is the village of Monschau; pedestrian only in the old part of town which winds up and down hills and along a river.

Aachen is wonderful, with much to see--and don't miss the bakeries, often featuring the famous Aachen gingerbread in various guises.

Aachener Printen! yes, Charlemagne's cathedral and there is also a museum with treasures (the Aachener Domschatzkammer). Very impressive. But generally speaking Aachen has a good vibe and interesting architecture just for walking around. We have been a couple of times and last time was the Christmas Market, which was enormous and well patronised. But you will enjoy it at other times too. Also the town hall - part of Charlemagne's palace became the town hall, but it is a nice building anyway.

Lavandula

Oh oops, I just saw you are going to the Christmas market - well, we loved it then, and you will have Aachener Printen in spades! My daughter also enjoyed Nutella crepes. We were there I think on the 23rd and it was packed to the gills. Fantastic vibe, enjoy!

Lavandula

Oh yes, Aggiegirl, do spend a lot of time in the Christmas markets of both Cologne and Aachen. My Son runs two of the sales huts in Cologne and one in Aachen each Christmas. Not allowed to advertise on this Forum, of course, but you might keep your eye open for those lovely handmade shawls and blankets that some enterprising chap goes to buy in the high country near Kashmir each Spring.