It is much cheaper to visit Austria from Slovakia. Obviously these two countries have a mutual deal to boost the tourism between two. I got a deal for Bratislava-Wien-Salzburg-Innsbruck (return) for 53euro (valid for 2 months, adlut price). Go to the Bratislava Main Train Station, Ask for Citi-Star. Enjoy!
We used the train to travel from Budapest to Salzburg and it was a most enjoyable yourney. The landscapes that you see along the way is stunning
You could go by local Postbuses (part of Oebb) from Salzburg to Lofer then St.Johann and Kitzbuehel for a scenic route. An other possibility would be Salzburg to Bad Ischl and Hallstatt.