We were trying to stay in Aachen (family of 4), but all the hotels near the station were only doubles hence we would need to book 2 rooms. Looking at staying in Cologne instead. Any hotel suggestions near the rail and Christmas market that would accommodate a family of 4? TIA!
Try Ibis at the Dom- Located right at the train station, steps from the cathedral. I stayed at the Ibis over Amsterdam Centraal train station and it was quiet. This Ibis has good reviews and I am booked here this December for the Christmas Markets. Ibis chain is basic, clean and generally well run.
You might try Coellner Hof. You don't say how old your children are. (am assuming 2 of the people in your family are children, otherwise, 2 rooms will be cheaper)
They have a 3 bed room available, so a bed could be shared if your kids are small
http://www.coellnerhof.de/zimmerpreise_guenstig_koeln.aspx?lang=en
B&B hotels have family rooms for 4 people.
https://www.hotelbb.de/en/koeln-frechen/roomtypes