Christmas Eve is the major family holiday and nothing will be open much past noon. My experience is that, other than places to eat, and not too many of those, you won't find much open in Nuremberg on the 25th. Some of the Christmas market, and the stuff around the train station mainly. But it's a great day to walk the city.
But if you want to see someplace different, you don't have to go to Wurzburg or Bamberg. And Rothenburg is a pain to get to from Nuremberg. Go just up the line to Erlangen. Or just south to Ansbach. Trains run about every 15 minutes. And those a really nice towns and will have nice Christmas decorations. But for something off the beaten path go to Amberg. Closer than Bamberg and really pretty. See the Stadtbrille, the Glockenspiel, the old marketplace. All the old town streets will have lights and decorations. And they have a nice holiday market. You'll probably be the only Americans there.