Perhaps you might start by contacting the Munich Tourist Office for what's ons.

Christmas Eve is the main day of celebration over the Christmas period and most shops and many restaurants close around 2pm on that day. Many restaurants will be open on Christmas Day but shops will remain closed. I can't recommend any restaurant in particular but I advise making a reservation when you know of one.
The Christmas Market on the Marienplatz should still be in operation on the day you arrive, although it's not one of the better ones in Germany it's still worth a visit, try the hot glühwein.
You could spend a day in the Alps or Salzburg. You can buy a Bayern Ticket on the trains for 27€ which covers up to 5 people for train journeys within Bavaria (also can be used for journey to Salzburg in Austria) there will probably be snow in the Alps.
As Alsa says the best thing is to contact the Munich Tourist Office.

Thanks ladies!

Glad to see i'm not the only one recommending Bayern Tickets! Just remember that they are not valid in IC/EC or ICE trains (the long distance fast ones!) but are also valid on buses and trams in most of Bavaria.

If you want to get up into the snow, Mittenwald (on the Austrian border above Innsbruck) is a good choice. Spectacular scenery and a nice village in its own right.

Nuremburg is also worth a visit but you need to pick the right trains, ie the Regional Express service that leaves Munich Hbf at 09:05 or 11:05 and a return that leaves Nuremburg Hbf at about 10 past the odd hours. These run at the same speed as the ICs but the Bayern Tickets are valid on them. A 5 person Bayern Ticket costs less than one ordinary return for this!

Thanks, Steve.