I'd start buy purchasing this excellent guide to ski resorts in the Alps:Where To Ski and Snowboard Worldwide: The Reuters Guide
Another good resource is the SkiEurope web site:SkiEurope
If you have to rely on public transportation and your time is limited, your choices will start to narrow. The easiest resorts to get to by train from Munich are Innsbruck, St. Anton, and Garmisch.
I think most people will agree with me that the Arlberg region is the best in Austria, but there are many, many excellent resorts in that country that rival in size and facilities, some of the biggest in North America. Ischgl/Galtur, Soelden/Obergurgl, Bad Gastein, Ski Zillertal 3000 (Mayrhofen, Hippach, Finkenberg and Tux), come to mind but there are others. There are also many smaller resors that would rank as large resorts in the Eastern US: Serfaus, Lermoos, etc.
For snow, the Arlberg/Ischgl/Solden usually have the best cover. For European snow weather, check out this siteSnow-Forecast.com
Also, you can get a discount at many reasorts in Austria if you join the Austrian Ski Federation. The Ski Austria card also gives you mountain rescue insurance. One of the easiest ways to join the Austrian Ski Federation is to join SKI CLUB ARLBERG:SCA
That's how I get my Ski Austria card.
You'll have a ball. Enjoy. SKI HEIL!
PS I re-read your post and noticed that you will be limited to 1 and 2 day trips. You might consider renting a car for these outings because train travel in this part of Europe is not as fast as car travel. By train, St. Anton is 4.3 hours from Munich (you must switch in Innsbruck). By car, it's only 2.2 hours. The car also would allow you to more easily get over to Zurs or Lech--generally less crowded parts of the Arlberg on weekends. I'll never forget the insanity of trying to get on the Naserien Gondola at St. Anton on a Saturday after a big dump. There were hords of powder hungry German day trippers pushing and shoving to get on the gondola. I felt like I was in the middle of a European soccer game...I should have skied Rendl that day (Zurs was inaccessible because the pass was closed). Saturdays, btw, are the the big travel days in Europe, and the trains can be packed, and difficult to negotiate with skis.
About the only easy train day trip from Munich is Garmisch. I hate cars and tried to plan my next trip without one, using Munich as my gateway city. I quickly discovered that most resorts in Austria are too time-consuming to get to by public transportation for international travelers looking to maximize their time on the Slopes. The Swiss resorts are better for those who enjoy trains--Davos, St. Moritz, and Zermatt are pretty easy to get to from Zurich by train.
Anyway, I wrote about the Arlberg last year for DCSki if you are interested:St. Anton ArticleLech-Zuers Article[ November 22, 2003, 04:53 AM: Message edited by: West Virginia Skier ]