We are going on our first Viking Cruise ending in Passau, Germany. The plan is to to stay on after and see Austria a little more. Tentative itinerary is for Saltzburg (3 nights), Hallstat (2 nights with a trip to Salzkammergut), Innsbruck (2 nights). We would plan to get the car for the Hallstat and Innsbruck portion of the trip. We are not married to this itinerary and so if there are any other suggestions of what others have done in the area we are definitely open to idea. Thanks so much. Any input is appreciated.

Passau - Hallstatt is about 3 hrs by train; change at Wels and Attnang
Hallstatt - Salzburg is about 2 hrs by train and bus; change at Bad Ischl
Salzburg - Innsbruck is about 1 3/4 hrs by train
Trains and buses about every hr

There are tons of other places which might interest you.
What are you looking for?

Thank you for the information. Do you feel we would be better served by having a car despite the availability of public transport or is it more of a hinderance with parking issues,etc? We are looking for a relaxing holiday, to appreciate nature and the landscapes. We may be interested in a museum here or there or visiting historic sites that are a "must see" but really we just want to be there and enjoy where we are the sights, the sounds, the culture, the people.....if that makes sense. I toyed with the idea of going to Slovenia after Passau but it just seemed like it was more of a hassle to get there this time around and maybe we should just enjoy Austria and save Slovenia to do with Croatia another time. We are open to suggestions.

People often prefer cars if they have a lot of luggage which makes train changes rather uncomfortrable.
All depends on your interests and on the time of the year. Actually it is snowing down in the Alps up to 1000 metres.
That can happen until April and may make car travel less attractive.

For Slovenia, I would recommend a car, as there is a fast motorway from Passau via Wels - Graz to Maribor whereas a train ride (with many detours and train changes) would take a whole day.

We drove all around Austria when we lived there (including to your proposed destinations) and did not find parking to be a hassle anywhere. Tourist vehicles are not permitted in Hallstatt; there is a spacious car park outside of the town.

This written, I might drop Innsbruck for the Salzkammergut cities of St. Gilgen and St. Wolfgang, especially if you're into nature. From St. Gilgen you can take the Zwölferhorn cable car up to the top for panoramic views and (easy) wandering. In St. Wolfgang one can take the Schafbergbahn (cog wheel train) up to the top, as well. Another alternative to Innsbruck is Seefeld in Tirol, where you can take the Rosshuttebahn up to the top for lunch with a view, and then wander down back into town.

As neckervd wrote, much of the advice depends on the time of year.