Austria in 2-3 days
If you’ve only got 2 days, base yourself in Vienna. If you’ve got three days, you could easily spend two days in Vienna, then take a late evening or early morning train (3 ¼ hours) to Salzburg.
In 7-9 days
If you’re not skiing or snowboarding, doing an east-west crossing is the way to go. From Vienna, head east along the Danube, soaking up the towns along the way. Further east, Salzburg and Innsbruck are both worth seeing, and are a good jumping off point for exploring the spectacular mountain scenery and towns in the Hohe Tauern National Park and the Tyrol regions, respectively.
Two weeks +
If you’re going to devote two weeks to Austria, spending a large chunking skiing or snowboarding is probably your best bet. Austria’s resorts and facilities are the equal of any around the world. If you’re not there in winter it’s still worth heading to the hills for walking or cycling or climbing.