Bamberg is a great city, as others have noted.
Regarding Christmas markets: I'd consider basing myself out of Nürnberg for several days if you really want to enjoy the Christmas markets. There are several great markets within the local transport zone that I think you'd find appealing. Rothenberg ob der Tauber is one (also a very famous walled city), Bayreuth and Bamberg will both have markets up, albeit smaller ones and if memory serves there is also a market in Ansbach, which is about 1/2 hour outside of Nürnberg. For transportation, all of these town are within the Nürnberg greater transport area (VGN) and can be accessed via the TagesTicket Plus. This is a 16.20 euro ticket that is good for 2 adults and up to 4 kids anywhere in the VGN zone. It is good until the next morning, and on the weekend, it is good for both Saturday and Sunday. It covers all S-bahn, bus, streetcar and underground lines (and DB regional trains) within the region. Fair warning: Nürnberg's market can be absolutely packed on the weekends.
From Nürnberg, I'd consider a day trip or overnight out to Prague, which has a very large Christmas market with a slightly different flair. You can get a DB bus direct from Nürnberg into Prague, tickets should be about 29 euro per person, each way (4 hour trip, give or take) on a comfortable bus.
Another option is to take the train or fly into Dresden and enjoy not only their very famous and large Christmas market, but the beautiful city as well.
Munich's market is OK but nothing to write home about. You may want to go further south into Austria and see what there is to see there instead.