what are good places to visit in Austria?

Answer 1

Vienna, Salzburg, Innsbruck, Graz, Linz are the biggest cities. Vienna and Salzburg have the most cultural highlights.
The lake regions in Carinthia and Upper Austria are beautiful. The mountains in Tyrol, Salzburg (state) are great for climbing. mountain biking, paragliding, hang gliding.
You see - a small country but a lot to see. Depends very much what you are after.
Vienna is a must - the rest is very much depending on your taste.