Hi Dale,
I've fished for many years in Austria and there are some nice rivers there. However, the biggest drawback
is the price of a license. It's quite normal to pay between 50-100 € for a day of fishing. There are even rivers
that are more expenisve than that. In some rivers there are almost no wild fish present, i.e. the fish populations are sustained by stocking.
I've fished the Gmundner Traun in Oberösterreich many times and I really like that river. It's probably the most famous of the Austrain rivers . But you will probably have a hard time finding the right places the first time you go there. The river Gail around the Lesachtaal in Kärnten is very nice. The Ager in Oberösterreich is also quite good. I can't recommend the Mur , since it's very popular with people who go rafting and canoeing and it ruins the fishing. I wouldn't care much if I payed 20 € a day , but it costs around 60 € .
I've never fished the Steyer or the Salza, they are supposed to be the best rivers in Austria, but very expensive indeed . Goiserer Traun is also supposed to be great and it looks great, but I've not tried it yet. My latest information is that it cost 86 € a day to fish there.
http://www.derfliegenfischer.at/index1.html (Austrian Site with a Forum)
http://www.freundedergmundnertraun.at/ (Site for the Gmundner Traun, Ebenseer Traun and Steyer Grünburg)
I don't know if you are fluent in German and understand Bavarian, but there are a few Stammtisches for Fly Fishermen in the Munich area.