Munich in December

The AT A GLANCE section here has some ideas:
https://www.ricksteves.com/europe/germany/munich
See what appeals to you.

A nice comprehensive list (with descriptions) of Munich's many Christmas markets.

https://www.munich.travel/en/topics/markets-festivals/christmas-markets-munich

Ron
Here is a potentially helpful prior post of mine about Munich. It’s from earlier this year.
I
am assuming that this is your first time or one of your first times visiting Munich. With that said, I would recommend not taking a day trip anywhere. There is so much to see in Munich, that you could not possibly see it in an entire week, much less two days. plan to go back. And plan to take many day trips on future visits to Munich. There may be no better city in Germany from which to take day trips. But if this is your first time, I would consider spending all of it in Munich proper.
I have twice stayed at Hotel am Markt. It is one of the best located hotels in Munich. And it is not extravagantly expensive. I have also stayed at Hotel am Viktualienmarkt for over a week. We really liked it. Great staff. A beer vending machine in the lobby tickled both my sons in law. Plus, it’s a great location to explore the heart of the Altstadt or the Gärtnerplatz/Glockenbachviertel.
I recommend that you take a walking tour of the old town. The one recommended in Rick Steves’ books or on his website is very good. I would also recommend obtaining either the day trips in Germany or day trips in Bavaria book by Earl Steinbicker. These have great recommended walks for Munich as well. Plus, they include many fantastic day trips and walks in other towns near Munich.You might also consider getting a guidebook for Munich beer halls, and beer Gardens, such as the Beer Drinker’s Guide to Munich. Try for the 7th edition. Beer culture is essential to an authentic Munich experience. Even if you don’t drink beer, go for the food, atmosphere, and get an alcohol free beer. The month of May may be a perfect time to enjoy a beer garden. You cannot go wrong with visiting any of the Augustiner beer gardens, the Hirschgarten, or any of the beer gardens in the Englischer Garten.
All of the “big” churches in the Altstadt are worth visiting. But not a lot of Americans make it to the crypt at the Michaelskirche or make it at all to the Ludwigskirche. The latter is a wonderful 19th century gem with many arts and crafts features. Plus it has a dynamite roof.
If the weather is poor, head to the Residenz or any museum. The Munich city Museum is unfortunately closed for renovations right now. So is the Neuepinakothek. This past December, my wife and I really enjoyed the Lenbachhaus museum. It is located in an artist’s Italian style villa. Some of the villa’s interior is preserved for your enjoyment. Plus the museum has one of the greatest collections of Blaue Reiter movement art in Europe. And a yummy cafe!
I think you would also enjoy a visit to the Neues Rathaus- a Munich landmark right in the center of the old town. You can visit some of the interior, as well as the courtyard. But the highlight is to take a ride up the elevator to the top of the tower for wonderful views, including the Alps. You should book your elevator ride online ahead of time. This will save you time and avoid a long line.
Some of the best traditional fare and Bavarian beer is at Andechser am Dom. Make a reservation to have dinner there. You won’t be disappointed.
Lastly, download the MVV-App. You can use this free app to get anywhere in Munich via public transportation. You can also buy your tickets or day passes on the app to avoid the confusing ticket machines. You can type in your location and enter your destination. And the app will give you several options to get there via public transportation. I use it all the time.
Have a ball!

Thank you for all the great suggestions. I have been studying the everything and have came up with some great ideas for things we may be able to fit into our three days.

If you have time, take the train up to Nuremberg and visit the site of the Nuremberg trials. You can sit in the courtroom and a movie is run of the actual trial and it's as if you're actually at the trials. It's well worth the train ride and it's really well done. And then the rest of the displays, etc. are fascinating and very educational. And then you can visit the Christmas market before hopping back on the train to Munich.