You could fly into Munich, visit the Berchtesgaden area (and Salzburg, Salzkammergut, etc.). Then head to the Innsbruck or Zillertal area and then to the Italian Dolomites. You could then head to Switzerland and the Berner Oberland and fly home from Zurich.
Our favorite place to stay, esp. since you mention cultural experience, is near Berchtesgaden.
Our favorites in the Dolomites:
You could do it in reverse. We have been using Lufthansa, as they have a non stop flight to NJ from Munich that departs Munich at approx. 3:30pm and arrives in NJ approx. 7pm. No need to stay near the airport or very early morning flights. Very nice. Last few times we stayed our last night in Berchtesgaden and Hall in Tirol (Innsbruck).
If departing from Switzerland, you could always spend the last night in Luzern and get to the airport in plenty of time for an early flight home.