Agree with your previous responses. I will add a few things. Yes, the westbahn train is well priced and especially great when you don't want to lock into a time for a OeBB train. Just know that you can purchase an advance ticket with OeBB for about the same price as Westbahn. I have not used Westbahn but I've heard it has become even more convenient. The Bayern train from Salzburg to Munich is well priced.
I was in all those cities twice in January. Loved our time there. We did have a lot of snow in both Munich and Salzburg so I'd recommend warm, waterproof shoes/boots. Both times Vienna was about 35 degrees which being from Minnesota I didn't think would be a big deal. But it is windy and chilly. The city blocks are like wind tunnels, and the churches are not well heated! But, Vienna just sparkled with the lights and snow. Look at Hotel Austria for Vienna. It's elegant and well priced and with the nicest, most expansive included breakfast I have ever had. In Munich, I once stayed at Hotel Uhland. It's a spotless, elegant refurbished mansion, also with a lovely breakfast.
I've done a lot in Vienna. The Treasury at the Hofburg is pretty special. The art museums spectacular. Make sure to go to the National Library. I tend to visit lots of churches. The Hapsburgs churches were interesting and obviously, St. Stephens, but don't miss Peterskirche in the same neighborhood. The Opera house is pretty spectacular inside. I'm not sure if there is opera in December, and I note that its not high on your list, but we got standing room tickets for a couple euro by waiting in a line behind the opera house (well described in RS guide) We did this mostly as a less expensive way to see the interior of the building and left at intermission. The Naschmarket is an interesting place to wander around especially to see the art nouveau buildings surrounding it.
The cathedral in Salzburg is one of the most beautiful I've seen. its bright with lots of Baroque (I think? perhaps, Rococo?) Mozart was baptized there. Some people pan the Sound of Music tours. I enjoyed it. I used my RS guide for a city walking tour and also did some research in advance looking for in town Sound of Music sites. I stayed near the train station. Hotel Hohenstauffen. I found it very well priced with a great breakfast. The owners are charming. It's a 15 or so minute walk to old town. In this situation, I liked being close to the train station especially since we had rolling suitcases and there was snow in the streets and on the walks.