I've enjoyed the Cologne Christmas Markets but I've not been there that late in December.

I found the Römisch-Germanisches Museum near the cathedral to be very interesting. Stuff from the days when it was a Roman town.

And go have a Kölsch -- Früh am Dom is the closest to the cathedral, Pfäffgen on Friesenstraße or Malzmühle at Heumarkt are better beers