Fritz and I took a weekend and visited the Christmas markets in Heidelberg and Ruedesheim am Rhein, both about an hour from Frankfurt by train. These were still quite popular, but no where as overcrowded as Frankfurt.
Heidelberg itself is well worth seeing - it's got a castle, lovely old town and a scenic bridge over the river. Another tip - we couldn't find a non-touristy, yet authentic enough restaurant with free tables, so we ate at the cafeteria in the department store. Good value for money and a great view of the city.
One thing I love in German Christmas markets are the kitch mugs. When you buy mulled wine or hot cocoa, you put down a deposit on the mug (rather than environmentally unfriendly paper cups!) and you can also keep them as souvenirs.
Rudesheim am Rhein is an adorable village in Germany's best known wine-producing region. We visited the market, then took a hike up to the top of the hill.
Dogs are widely excepted in restaurants in Germany, but some go the extra mile (or kilometre). The sign here says that dogs are heartily welcome.