Servus aztimm

I lived in MUC for quite some time. Let me answer some of your questions, I will leave the rest to others, also do some research on Flyertalk, MUC is quite popular to go to in Germany, especially for Americans.

It will be a piece of cake for you to find a Christmas market. The biggest one is always on the Marienplatz where the Glockenspiel is. Also, Hofbräuhaus is nearby. My experience is that it's nothing special but it's a MUC attraction, so why not go there for one meal time?
I would also suggest to take the U-Bahn out to Fröttmanning to take a tour of the new soccer stadium of Bayern München and 1860 München, the two Munich soccer teams. If you are into sports, this arena is really amazing and worth seeing. If you fly in or out of MUC while it is still dark outside and you have a window seat, watch out for a red / white / blue lighted outside arena nearby the airport and an Autobahn.
Another site that I haven't seen yet but I plan on doing so in January is the new BMW World. You'll find plenty about it on the internet.
The old Olympia park (MUC held the Olympic games in 1972) is nice, too.
How about some lakes? Take the S-BAHN to Starnberger See and take a boat ride (if still available in December) but bring a nice warm jacket.

There is so much you can do. If you need to know anything, let me know or ask here. There are plenty of locals and experienced MUC travelers that can help you.

Enjoy your stay, make your own experience with MUC beer and let us know which brands you've preferred.

Pfirti (Bavarian for cheers!)

supermasterphil