Mardee,
My suggestion is a bit different. Given the short time frame of your trip and the fact that you're travelling by train, I'd suggest focusing on Salzburg and Hallstatt this time (unless there's some overwhelming reason you need to visit Vienna).
Salzburg is a great home base for exploring other parts of that area, and of course has lots of Mozart history. I found the large Fortress on the hill above town interesting and I spent an afternoon exploring (provides great views of the city).
One other thing to consider is the travel times. Unless you take a day tour to Hallstatt (Bob's Special Tours, etc.) you'll need to allow about half a day for travel times to Hallstatt each way. You'll change trains in Attnang-Pucheim (usually a "layover" time) and then of course the short voyage on Stefanie across the lake. Buy your tickets for both trips in Salzburg, as the small rail station in Hallstatt is not staffed (there may be a ticket machine, I didn't check).
While in Salzburg, you could also take a day trip to Berchtesgaden which is beautiful alpine town (and of course has a somewhat "colourful" history as well).
I'd recommend at least two nights in Hallstatt. Not only is it a very beautiful location, but there's lots to see as well. The tour of the Salt Mine is interesting and stopping for a "cool one" at Rudolfsturm (the large Castle at the top of the Funicular) after the tour provides an incredible view of part of the town and the lake. There's also a Musuem that chronicles the 5000-year+ history of the town (it's apparently older than Rome). You could also rent a small boat and take a trip on the lake, a very way to spend an afternoon. It's a great place to relax and unwind from strenuous travels in other locations.
Happy travels!