I am in Munich a few times every year for work and can answer any questions you have.
You are correct that the main Xmas market is down near Marienplatz. Just remember that the last day of the markets is the 24th around noon. This is when Germans celebrate Christmas (Heiligabend - Holy Evening) and not so much the 25th.
Many Americans (and tourists) can be Xmas market junkies. There are thousands of them in Germany and each one is different in its own local way.
The highlight of the Munich market IMO is the giant Xmas tree located in the courtyard behind the Rathaus. Otherwise I was honestly wasn't too impressed with it.
General Munich highlights for me include...
-Olympia Park / BMW Welt (BMW factory tour if you plan ahead.)
-Visiting the brew houses of the six main Munich breweries. I personally avoid the Hofbräuhaus and prefer the locales that serve Augustiner beer.
-Attend the Munich Opera
-Visit the Deutsches Museum (
other museums in Munich)
-Walk through the English Gardens
-Visit the Munich city palace of Nymphenburg
-Catch a Bayern München football match if you can afford it
-Eat a real Brez'n (pretzel) and white sausage before noon with sweet mustard (Weisswurst).
I think your idea to use Munich as a base and then radiate out using rental car/train is a great idea. Nearby highlights include...
-Visit the ANDECHS monastery and brewery (Half-day trip)
-Visit the Concentration Camp in Dachau. Obviously this is quite sobering and educational. (Half-day trip)
-Visit the nearby town of Erding. Here you would find a cozier, smaller-town Christmas market. You can also visit the famous indoor waterpark,Therme Erding. You can also do the Erdinger brewery tour with beer drinking. When I did this tour in 2011, it cost me 10 EUR and included a 45-minute tour followed by 3 hours of unlimited beer drinking, pretzels, and white sausage. (Day trip)
-Visit at least one of the famous "fairytale" castles of King Ludwig II. These are Neuschwantein near Füssen, Linderhof near Oberammergau, or Schloss Chiemsee on the Herrenchiemsee island. While Neuschwanstein is the most famous, it was never finished and is the most touristy. Linderhof is the only one he finished and you can combine a visit there with visits to Oberammergau and the Ettal Monastery. The Chiemsee palace is cool because you have to take a boat to the island and the place is an incomplete replica of Versailles; its Hall of Mirrors is even larger than that of what the Sun King enjoyed near Paris. (Each of these is a day trip)
-Visit the Eagles Nest in Berchtesgaden. (Day trip)
-Visit the most famous and most touristy of the German Christmas markets in Nürnberg. Eat some of the famous Nürnberger bratwursts. Visit the famous
toy museum. (Day trip)
-Visit the oldest (and perhaps most beautiful) German Christmas market in Dresden and visit the famous Frauenkirche (Day trip)
(
A lot more information on all German Xmas markets.)
-Visit the town and brewery in Tegernsee.
-Obviously if you want to turn this into some sort of winter sports/ski vacation, it would require a small book of recommendations, so I am assuming this is not your goal.
-I highly recommend using
AirBnB to find a place to stay. You might consider looking at areas of Munich that are a little outside of the downtown area. Perhaps the Pasing neighborhood?
-Remember you can also stay at smaller German "Pensions" (Gasthof). These are cozy, small inns, that tend not to have large websites or be affiliated with large hotel booking sites. But they tend to be inexpensive.
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Learn this map.
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Learn how to use this website (even if you buy a Germany Rail Pass)