Remember the beautiful countryside in The Sound of Music? That's Austria, a German-speaking country that once ruled over most of central Europe.
Vienna is a gorgeous city, rich with history. Take the time to walk around, vice using the U as most things are within 10-15 minutes of each other (besides, might as well walk off all the delicious food). Vienna International Airport is on the outskirts of the city, meaning either a bus, train, or cab ride (~35 euro) into the city center. Definitely take the time to see Stephansdom (St. Stephen's Cathedral), Hofburg Palace (Treasury, Spanish Riding School, Sisi Museum, Imperial Apartments, Silver collection, among others), Schonbrunn Palace (the Summer Palace--a little ways outside of town but with a Versailles-like garden), and any one of a host of classical music concerts. Vienna is a surprisingly expensive city, so try to keep that in mind when planning your time there.
- Opera - Vienna's State Opera house is beautiful and hosts a different opera nearly every night. Cheap obstructed view tickets are often available, and even cheaper standing-room tickets go on sale 80 minutes prior to each performance (ticket window on the left side of the opera houe as you face the front). For most of the 2010 season, they also broadcast the opera live on the street on a big screen. The somewhat short tour is worth it for opera/theater fans, who get a sneak peak of the huge backstage.
- Other Concerts - You will be mobbed by folks in period costumes schilling various touristy concerts featuring the Best of Mozart and Strauss. While fun, they are definitely touristy and expensive (at least 40 euro). The tourist information office can give you a more comprehensive list of concerts during your stay.
- Gasthaus Ubl - Pressgasse 26, not far from Naschmarkt. Real, delicious Vienese favorites in a place frequented by locals, with good prices. Handwritten daily specials in German.
- Trzesniewski - Dorotherg 1, in the Old Town. Famous snack-shop with dozens of cheap (1 euro) open-faced sandwiches.
- Sachertorte - this dry but chocolatey dessert is famous, and you can try the original at the Sacher Cafe (actually 3 cafes, each with a different ambiance and slightly different menu) near the Opera