Any recommendations for Scenic Train Rides in Austria?

I want to take a scenic train trip this coming June and am considering one of the Swiss train rides from Lucerne to Montreux. However, this would take me far from where I want to spend the rest of my trip, namely at least a week in Vienna and then on to eastern and central Germany. When I read in a recent post that the Austrian alps are just as beautiful as the Swiss I thought that this may be the answer to my desire to avoid having to return from Montreux. Now, the question is: are there any train trips through the alps, perhaps originating in Salzburg or Vienna that someone can recommend? I don't want to do this by car, even though I've done quite a bit of mountain driving in the U.S. Another option could be a train ride from Innsbruck to Bolzano or Merane in Italy. Has anyone done this and can recommend it? Looking at the map, that would certainly keep me closer to where I want to be. I'm just beginning to plan the trip and am somewhat overwhelmed by all the options. Any suggestions will be greatly appreciated.