Christmas in Germany with kids

"Our focus is: budget, a small town feel, family friendly accommodations (restaurant on site, open on Christmas eve/day is ideal)."

You will probably need to adjust your expectations. Christmas is taken very seriously in Germany. Small-time innkeepers typically do not prepare meals for guests on holidays - they're with their own families. Normally the only dining options for visitors will be major hotel or airport hotel restaurants and train station food. With "budget" as the first item on your list of criteria, you'll probably want to see about a holiday flat where you can prepare meals independently.

That is a tough one. Things will be pretty quiet in Bavaria from the 23-26th.

You best bet is to head to one of the areas with good tourist infrastructure.
Garmisch-Partenkirchen
Allgaü (Obersdorf or Oberstaufen)
Bad Tolz Area (Lenggries, Tegernsee)

Also, will you have a car or not? Some of these small town places are not very accessible without a car.

Another possibility is just heading to Munich, will have more of a "small town" feel than Hamburg and plenty of restaurants will be open.

DJ

Christmas Eve is spent with families in Germany and unless you are in a hotel that is offering a Christmas Eve dinner, you will not find anything open after 14:00 on the 24th, except for places in the airport and big train stations. This is not going to be budget friendly for you, nor much fun for 2 small children. The resort places where there might be snow, like in Garmisch for example are probably all booked up now and they also won't be budget friendly.

If you are in Hamburg, stay up north. There are lots of beautiful small towns and villages up there and it will save the travel time and travel money heading all the way to Bavaria. Perhaps Potsdam or Lübeck?

With such small children, it would be lovely to do something in Hamburg instead of traveling far away. Most churches have nativity plays on Christmas Eve that your kids would enjoy. Many of the Christmas Markets in Hamburg are actually open after Christmas. Their website is in German, but you can get a good idea and see the dates.
http://www.hamburg.de/weihnachtsmarkt/

I agree with Russ...definitely rent an apartment so that you can have your own family celebration with your children and cook a nice dinner. Most commercial eating establishments will be closed and those that are open won't have the ambiance that I think you are picturing.
Attend a Christmas service, find a Christmas market with lots of lights, toys, and warm things to eat! Build a snowman in the park! Bring some presents along and make it family occasion. Your kids are little - they'll love anything festive and out of the ordinary!

Maybe Reit im Winkl. There may not be too much snow in December, even though Reit im Winkl is known as a "snow magnet." http://www.reitimwinkl.de/

As mentioned, for stays under a week at this time it may be hard to find a place. From Reit im Winkl you could drive to surrounding areas from here as a base (Ruhpolding, Aschau etc.). We stayed here in an apartment once: http://www.beim-wimmerbauer.de/ There are several restaurants in the town all within walking distance.

Hiked here in summer from the town center and this could be fun too with a Hütten Abend. I think there is a bus to get you there too and sled ridding with snow: http://www.hindenburghuette.de/ Webcam is here overlooking the Chiemsee: http://www.hindenburghuette.de/7.0_webcam.html

Winklmoosalm is nearby too for skiing other than in Reit im Winkl: http://www.winklmoosalm.de/

Rosi Mittermaier the alpine ski racer and overall World Cup champion in 1976 is frrom Reit im Winkl.

Oberaudorf could be an idea too... http://www.oberaudorf.de/

Consider staying at Gaestehaus Richter in Oberammergau. We stayed there in mid-December with our kids two years ago when they were just a little younger than yours and highly recommend it and the price was excellent. The Gaestehaus is in a residential area just on the edge of the more commercial/tourist area and everything is within very easy walking distance. We were the only guests staying there at the time there is a small kitchen and she very happily allowed us to use the breakfast room whenever we wanted, so we were able to cook small meals for the kids. They don't have a restaurant but her family is heavily involved in tourism in the area and she will know where you would be able to eat on these holidays and what other special activities (sleigh rides and church services come to mind) might be available over the holidays. The Gaestehaus is very close to the train station, if you are traveling by train. She even brought out some of her grandson's toys for the kids to play with while we were there.

For us Oberammergau was the right blend of small-town, old-world Christmas feel and close enough to all the local attractions. It is on a side rail-way line so may not be central enough for you, depending on what you want to see and how you are traveling these days but it sounds like the perfect fit for what you are looking for.

Shouldn´t be a Problem! Our Family does go every year on the 25 or 26th(or both) dec with the whole Family.
But you Need to book early,

There are to many places from Bacharach to Leipzig, from Berlin to Mainz

If you are in Hamburg, stay up north. There are lots of beautiful
small towns and villages up there and it will save the travel time and
travel money heading all the way to Bavaria. Perhaps Potsdam or
Lübeck?

And I agree with Ms. Jo. There is no need to travel all the way down to (Southern) Bavaria (more than 8 hours by train). If you want mountains and quaint towns there is a equally picturesque region much closer to Hamburg: the Harz mountains. They offer several perfectly preserved towns with literally thousands of half-timbered houses, like Goslar, Wernigerode, Quedlinburg, Stolberg, Wolfenbüttel, Einbeck or Duderstadt. Quedlinburg and Goslar are World Heritage Sites, and from Wernigerode you can take a steam train up to the highest peak of Northern Germany, the Brocken.
Here is a gallery with 140.000 pics of the region (have a look at the mentioned places):
http://www.raymond-faure.com

Thank you all for the advice! Greatly appreciated.

We were in Germany for Christmas last year and plan on going to as many Christmas Markets again! Nuremberg is a must. The primitive market in Guteneck is unique. Dresden and of course our favorite town, Munich is wonderful! We went to over 12 Markets in southern Germany and Prague! All were wonderful and different!

We drove everywhere with a rent car and plan on it again! We will travel to Berlin this time and drive south to Munich!