I spend a few days at Christmas market destinations every year, so I've been to many by now, both in what is now Germany proper and in the German-influenced periphery.

I agree with those who recommended Strasbourg (and Colmar), Dresden, and Cologne. Last year I did Innsbruck, in the Austrian Tyrol, and Bolzano/Bozen, in the Italian (but predominantly German-speaking) part of Tyrol. I found the combination very satisfying, and had a great time in both cities.

I'm in the preliminary stages of planning this year's trip. I'm thinking Hamburg, Bremen, and Lübeck.