This is not so much an attraction as an extremely useful transport to save you from taking long and winding paths up to the top where the museum and a few other attractions are. One round trip is free with the Salzburg card. Otherwise it's E3.60.
As others have noted, the elevator deposits you right at the one of the filming locations of the Sound of the Music. Directly behind you will be the Modern Art Museum. There's another restaurant not too far away. Both were totally full while we were up there around lunch time. Walking through the park on top of the hill will lead you to other historical structures as well as the Salzburg water works.