Nuremberg has a number of medieval sites, such as the castle and the city walls. As I think you are already aware, it doesn't have the quaint, stone and half timber town center like a Rothenburg ob der Tauber.
There is one primary Christmas Market https://www.christkindlesmarkt.de/en/
I don't know if you have traveled with this group of four or how long you will be in Munich. If I did I would suggest that you strike out for a day on own to Rothenburg. Personally, I have found that when traveling with a group of family or friends for more that a 3 or 4 days it is very worthwhile to include a day of where the group can split-up and go different ways. I am traveling with my daughter and her husband to Munich, Innsbruck and Salzburg for a bit more than a week in December. We have built 3 half-days into our itinerary where we split-up and do some different things based upon our interests.