One of your first stops should be Haus der Berge. Here, you'll be able to orient yourself and get lots of useful information before you begin exploring.
When you've finished exploring this tourist information center in Berchtesgaden, why not make your way to Eagle's Nest, Hotel Zum Turken WWII Bunkers, and Bad Dürrnberg Salt Mine? They're not far from Haus der Berge and also popular with many tourists.