I agree that this should have been a combined natural and cultural site.
I stayed at Obertraun and took a ferry from there to Hallstatt Markt, returning again later by bus from Hallstatt Lahn.
The bus also took me up to the Obertraun cable car station from where I was conveyed in two cars to the summit of Krippenstein, a part of the Dachstein Massif. I hiked from there to the 5 fingers, a lookout that is cantilevered over the edge of a 400 metre cliff. The views over the Hallstattersee and the Dachstein massif were extensive.
Descending by the upper cable car I then visited the Ice Cave, a much larger series of ice filled undergound galleries than I had expected. The formations into which the ice had contorted itself was fascinating.