New York City
We'll be in Munich and then Salzburg in July. Which is the best location of the two to do some Alp related activities? And any recommendations?
Salzburg is much smaller - and although at the edge of the mountains, most of the (big name) destinations mentioned by others are actually faster to get to from Munich. All of the mountains near Salzburg go "in one direction", whereas Munich is centrally located between the "Salzburger Land" and Haus Tyrolia. Its worth mentioning that even if you live in Salzburg, you drive through Munich to get to Tyrol (almost: Rosenheim).
Also - many of the best spots for hiking or climbing are in the area of Innsbruck - which is more or less directly south of Munich, and much closer to Munich than Salzburg.
Train service to either Salzburg or Innsbruck from Munich, and in the region in general is not that great. (All those mountains make for tough railway travel) The best options for getting to the Alps by train are certainly all out of Munich, with both the Deutsche Bahn AG DB Systemtechnik and several private rail services running hourly or half-hourly services from the Main train station in Munich. Train service in Salzburg is neither as extensive, nor as comfortable.
Garmish, as has been mentioned, is an easy train ride from Munich, and is a center for all things alpine.
For more picturesque, but less arduous activities, the Tegernsee south of Munich is one of the most beautiful spots in the alps....and as of yet, not as frequented by hordes of American and Japanese tourists - but very many Germans.
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However, the mountains are just more present in Salzburg and it's quick and easy to get deeper into them. You could, for instance, go to Hohe Tauern where you'll see the highest peak in Austria, the Grossglockner. I'd also highly, highly recommend you drive through the Salzkammergut lakes region. The best-known spot on that route is Hallstatt but the other villages along the way are spectacular as well. You can head over to Innsbruck to see another gorgeous city with a backdrop of mountain scenery. If you really want to get out for some alpine hiking, maybe consider the Eagle Walk, which is in the Tirol state/bundesland (where Innsbruck is located). It's a very long trail (250-some miles) that's broken up into multiple stages, at varying levels of difficulty.
Oh, I'm a little jealous—I love this part of the world! There are so many scenes that pass by, even when you're sitting on a train, that look like something out of a fairytale. Gute Reise!
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What activities? If you are into hiking and other outdoorsy adventures, start in Garmisch-Partenkirchen, Germany or Reutte, Austria. Also look into Berchtesgaden, Germany, although that town is much easier to utilize with a car. If you must choose a city, Salzburg is closer to the Alps. From Munich it would take about 2-2.5 hours by train each way to reach a town at the foot of the Alps.
If you're not into hiking but just want to see the Alps, from Salzburg you can take a cheesy-but-worth-it Sound of Music Tour (recommended: Bob's Tours). This will show you a lot of the Alpine landscape as well as the lake district of Austria.