Here's a 7-day guide, filled with suggestions on how to spend a week-long trip in Vienna.

Day 1: Altstadt ("Old Town")

Explore Vienna's historic old town!  Highlights can include:

• Domkirche St. Stephan - This 12th century cathedral is Austria's grandest. Climb the 343 spiral steps to the top for Vienna's best view.
• Staatsoper - This French Renaissance style building is Austria's premiere opera house. Take in a performance if time allows.
• Ringstrasse - Take a streetcar ride around the Ringstrasse which encircles Vienna's Old City.

Day 2: Hofburg Palace

This was the winter palace of the Habsburgs, and you could spend more than a day here alone. Try seeing some highlights, such as the Imperial Apartments and Imperial Treasury. Other highlights to see:

• Albertina - This 18th century palace contains an extensive collection of graphic arts, featuring a series of drawings by Durer.'
• Augustinerkirche - This 14th century church was the parish church of the Habsburgs. Visit the elaborate tomb of Archduchess Maria Christina.
• Spanische Reitschule - The Spanish Riding School is where the famous Lippizaner stallions perform.

Day 3: Museums

See two of Vienna's finest museums today:

• Kumsthistorisches Museum - This museum stands across from Hofburg Palace and holds much of Europe's great art, most of it belonging to the Habsburgs.
• Liechtenstein Museum - This newer museum, open since 2004, is housed in a spectacular baroque mansion and contains the treasures of the Liechtenstein family.

Day 4: Shopping

Take a break from sightseeing to do some shopping! Options abound, try:

• Karntnerstrasse - This is Vienna's main shopping street, comparable to New York's 5th Avenue.
• Naschmarkt - Just south of the Ring, this is Vienna's most famous open-air market.

Day 5: Schonbrunn Palace

This was the summer home of the Habsburgs, and has an amazing 1,441 rooms. Don't miss the State Apartments, Imperial Gardens and the Gloriette (marble summerhouse).

Day 6: Palaces and Museums

More Viennese attractions you won't want to miss:

• Schloss Belvedere - Belvedere Palace sits on a hill with an excellent view of the city. It was once home to Archduke Ferdinand, whose assassination set off World War I.
• MuseumsQuartier Complex - This complex holds many attractions, including several museums featuring modern art, a tobacco museum and a children's museum.

Day 7: Danube Day Trip

Rent a car and head west along Route 3 on Austria's "Romantic Road," which runs along the northern banks of the Danube. Ideas for stops:

• Krems - This 1,000 year old medieval town features cobblestone lanes and arched gateways.
• Durnstein - Best known wine town along the Danube.
• Melk Abbey - One of the finest baroque structures in the world.