If you ever want to make an Austrian cringe, start singing 'The hills are alive with the Sound of Music'. The film that forever ingrained Austria in the minds of Americans is something of a sore spot in the country itself. If you go to Austria expecting to see families singing in the mountains you will be greatly disappointed. Most of the film was made in Hollywood and many of things that happened in the movie didn't occur in real life.
What to do
Austria these days is a modern country that is the essence of sophistication. The mountains still exist of course and if you visit Salzburg you can even go on a Sound of Music tour. Save your money and instead go on a trek in the mountains or just hang out at a cafe. You will learn more about Austria that way than you will on a silly tour.
No visit to Austria is complete without at least a few days in Vienna. A cultural capital in Europe for centuries, modern day Vienna mixed hipness with history. You can spend all day wandering around historic buildings and all night enjoy fine wine, music and dancing. You can listen to the Vienna Boys Choir, see where Mozart made it all happen, and admire how every single person in the city has a mobile phone.
If mountain scenery is your thing, you might want to make a trip to Innsbruck. Towering over the quaint city center is the ski jump used in the 1976 Olympics. You can climb up to the top and see how crazy the ski jumpers really are. You can also visit the gym in the city where Arnold Schwarzenegger used to pump iron. There are lots of creepy poster of him on the wall to inspire you.
Austria is extremely central for many European travelers so it's an excellent stop for those on a Eurail Pass. You can book a flight into Vienna International Airport (code: VIE), which is by far the largest and usually the cheapest airport in the country. You can also fly into the Salzburg W.A. Mozart International Airport (code: SZG), which sometimes has good deals from within Europe.