The Salzkammergut is lovely, and has lakes and mountains as well as having Salzburg
, but Tyrol was the place to go for British tourists visiting Austria in the Edwardian and inter-war periods. If EBD hadn't gone to Pertisau, she'd almost certainly have gone to one of the other Tyrolean resorts ... and presumably a lakeside resort, because I don't get the impression that she was one for climbing the Alps
Vienna is amazing, but capital cities are always expensive and I don't think it's somewhere that a person on a limited budget would have visited for more than a couple of days.
If the school hadn't been in a lake/mountains area, the link-up with the San would presumably never have happened ... maybe Jem would have been a diplomat, or a businessman.