What to pair with Munich in winter?

I vote Vienna! NYE there is supposed to be awesome. It's on my bucket list.
Safe travels!

Exactly how many total nights do you have? If its only a week or so, If it were me, I'd just head south from Munich to the mountains (Berchtesgaden = Eagles Nest), or Salzburg.

Easy train - Vienna, Salzburg, or Nuremburg.

While in Munich - use TOP HAT TOURS for a day trip to Dachau Concentration Camp - he is amazing. He also does a great Walking City Tour - you'll learn a ton with him.

Radius Tours also does a great day trip to Regensburg from Munich.

While in Munich, make sure you take a 30-minute train to Dachau for a half day. Another good day trip is Salzburg (2h).
When you say you’re going to Munich, does this include exploring the Bavarian Alps too? If yes then take a direct train to Füssen (2h 15m) and sleep there. Neuschwanstein Is a 15m train ride away. You can then walk over to Hohenschwangau (30m). The next day take a bus to Oberammergau (1h 45m). Why miss this opportunity when you’re nearby?
Vienna and Budapest can be seen on another trip since you can take a direct train between the two cities taking a total of 2h and 45m. I would also include a day trip to Bratislava from Vienna.

Vienna sounds like a good bet. We enjoyed a few days before Christmas there with our kids and it was so nice to stay in the Ringstrasse and walk around without traffic. When you're cold, visit one of their famous cafes for cake and coffee! They have amazing Christmas markets there as well.

Nuremberg. Much better in the winter than Munich or Salzburg (although I like both of them too.)

Nuremberg has more WWII history, is a beautiful city, and is close enough you don't waste a lot of time getting there. My other suggestion would be Prague, which I like best in winter when it's got snow.

Berchdesgaden is closed in winter, but if you want to ski you can go south from Munich. Garmisch is open and good for a couple days.

If you go to Nuremberg check to see if they will light the city walls of Rothenberg on fire for New Years Eve, and if they do take a cab and go there. It's a lifetime memory.

The next day take a direct train to Oberammergau

Originally I misread that and thought that the suggestion was to go to Oberammergau from Füssen. If that had been the suggestion, Oberammergau is reachable from Füssen in just over 1:30, but only by bus. By train it involves going all the way back to Munich with a couple of changes and takes well over 4 hours.

To go to Oberammergau from Munich can be done by train but the RB63 is the only train which serves Oberammergau and it only shuttles back and forth between Oberammergau and Murnau. Munich to Murnau is on a RB6 train to Seefeld in Tirol (Austria) via Murnau, Garmish-Partenkirchen and Mittenwald which are all lovely towns.

There is a bit of a wait in Murnau waiting for the Oberammergau train.

"...next winter, right after Christmas through the New Year. He is really into history (especially World War II history), technology, and good food."

Most visitors to Germany believe that after Christmas, Christmas and the Christmas markets are over. Not completely true. I suggest you hop on a train in the direction of Stuttgart (about 2 hours from Munich.) Near Stuttgart is the town of Speyer, where Christmas lives on into the new year. Speyer also has the Technik-Museum - open year-round normally - and one of Europe's finest examples of Romanesque architecture - a UNESCO World Heritage site, actually - the Speyerer Dom. And of course Stuttgart itself has some good options, including the Mercedes Benz Museum and the Porsche Museum. And in nearby Ludwigsburg you'll find Schloss Ludwigsburg.

Have you considered taking a day trip out of Munich to Nuremberg? We spent three nights there a few years ago during the Christmas Markets and thoroughly enjoyed the smaller town feel. There are many sites connected to WWII, including the Documentation Center that puts the rise of Fascism into context of the world at the time. Not political but thought provoking. There are many other sites worthy of a couple of days, but it is easily doable as a day trip from Munich by train, approximately one hour.

Of the four possibilities you mentioned Luzern is the only one I can address. Visited there as a day trip a few years ago - it's beautiful and wish we would have spent a couple of nights.

The next day take a direct train to Oberammergau

Nigel, I edited my post. According to Deutsche Bahn, there is a direct train from Füssen to Oberammergau taking less than two hours.

MaryPat, can I suggest one last peek at Deutsche Bahn. Isn't the timing for a bus?

Salzburg and Vienna combo is a perfect “few days” option. Same train line and very different Austrian cities.

MaryPat, can I suggest one last peek at Deutsche Bahn. Isn't the timing for a bus?

Nigel, it says bahnhof that translates to railway station.

normally if DB uses the word Bahnhof (which you are right, it does mean train station) that is usually the name of the bus stop at the station. If it is for the train it just has the name of the station, usually the same as the town.

The DB online service shows the route, regardless of mode of transport. It is possible to adjust that so it only shows trains, even what type of train, but the default looks for the quickest solution among boat, train, bus, S-Bahn. U-Bahn, taxi and straßenbahn.

You probably saw something like:

Bahnhof, Füssen 12:45 1:38 0 BUS Fares not available
No OnlineTickets possible
Bahnhof, Oberammergau 14:23

which is for a bus, specifically

Bus 9606 Bus Direction: Bahnhof, Garmisch-Partenkirchen
Behindertengerechtes Fahrzeug
Operator: Regionalverkehr Oberbayern

The train from Füssen to Oberammergau (after the faster bus is deselected) shows something like:

Füssen 10:05 4:07 2 BRB, RB 25,00 EUR 41,30 EUR
Oberammergau 14:12

which indicates there will be 2 changes and it will be over both BRB (Bavarian regional trains) and RB (DB regional trains). You even get a fare quote. The start and finish points are just a few metres apart from the previous solution - one on the rails and one on the road outside. The first change is at Munich Pasing and the second at Murnau.

I hope that explanation of some of the more esoteric uses of the DB travel planner helps....

By the way - the term "Behindertengerechtes Fahrzeug" means that the trains have facilities for disabled passengers.

Thank you Nigel for pointing that out, you just taught me something; much appreciated! I think I better edit my post.