The best Christkindlmarkt in my opinion, is in Nurnberg (nuremburg) Germany. It is an old, traditional market with all the fun food, drink and gifts, plus the nativity set right in the middle. It is located outside the cathedral and is just a beautiful setting on a cold, December night. But there are so many to choose from - another favorite of ours was in Trier Germany. Trier is a beautiful city all by itself with remains from the Roman times and they do a fabulous Christmas market as well.
Another really nice city is Koln (cologne) - they have a couple of Christmas markets in different parts of the city - one near the beautiful cathedral. It is really easy to ride the train from anywhere in Germany to get to them.
And then there is the wonderful little town of Seiffen that is in the East (south of Dresden) which is where the nutcracker was born! This little town is fantabulous during advent (really anytime of the year). They have a Christmas market, but really the fun is just visiting the city and all the little workshops where all the nutcrackers and smokers and wooden toys are all made.
But I also have to agree that the Birmingham Christmas market is outstanding. We would visit at least 2 times per week either during the day or evening to just have the schwenkbraten (pork steak on the swinging grill) or dampfnudeln (steamed dumpling with vanilla sauce), a little gluwein (glowing wine) to drink and warm you and do a little shopping (polish pottery and other little gifts).
Wherever you choose, I think you will have a fun experience...have fun