Salzburg – old town, Mozart haus, fortress up on the mountain, maybe even the Sound of Music tours (mind you, in the final scene, they actually walked into Germany for the film). Werfen ice caves to do on a day trip or drive down by car. 2 steep cable cars, walking in between and also lots of walking in the caves. Bring your gloves and a warm jacket, it will be icey cold in the caves, no matter the weather outside. Open only in summer (May – October?)
Lake district – Wolfgangssee, lots of different things to do, Halstatt (very famous, very picturesque), Mondsee
Vienna, try wiener schnitzel (they’re biiiiig! Share if possible), lots of beautiful old buildings. If you have the time (a full day) you could do a day trip to Bratislava in Slovakia (add another country to your list), only about 1,5 hours by train for about €15 return, interesting because similar style of buildings, but not as well kept up as in Austria. Different currency, but they accept Euro’s too.
Skiing, lots of different places, different gradients. Different difficulty-system than the States, green blue red black. Cheaper than Switzerland, and still beautiful.
Eat and drink: the wiener schnitzel, schnapps, kaiser schmarrn (kind of pancake dessert)