Well I understand that a six hour ride even on a train that's as comfortable as the German ICE after an intercontinental flight would indeed be a nuisance.

I don't think the sights in Austria are "better than Berlin" - just different. And they are closer to Munich, easier to reach.
There is enough to do and see in and around Berlin for a whole week. Two days would actually be a very short visit for such a city.

My general opinion is: Less is more. Better go to less places and stay longer, get to know them better. There is enough to do and see in and around Munich for a whole week as well.
Perhaps it is better for you indeed to stay in Munich and choose two or three day trips from there.
That way you'll be in Munich while the famous Christmas market is still open (till Dec 23). You'll enjoy it, I'm sure.

If there is snow in the mountains a day trip to Austria or to the Allgäu, perhaps Garmisch-Partenkirchen, would be a nice altrnative.

By the way, the weather in December can be quite uncomfortable. Bring warm, rainproof coats/jackets, scarves, good winter shoes and umbrellas.

Restaurants at Christmas: Many of them will be closed. Others offer special holiday meals but require reservation in advance.