Spend your first day in Vienna at the Schönbrunn Palace, the former summer residence of the Habsburgs. Explore the palace's beautifully landscaped gardens, which are open to the public free of charge. Visit the Palace's interior to learn more about the history of the Habsburgs and the Austro-Hungarian Empire. Be sure to check out the on-site attractions, such as the Maze and the Gloriette, which offer amazing views of the palace and the city.
On your second day in Vienna, head to the Kunsthistorisches Museum, one of the world's most important art museums. Spend hours exploring the museum's massive collection of paintings, sculptures, and decorative arts from the Renaissance to the Baroque period. Don't miss the gallery of Ancient Egyptian and Near Eastern art, which features the famous portrait of Nefertiti. End your visit at the museum's café, which is as much a work of art as the museum itself.
If you have more time, consider visiting the Belvedere Palace, the Vienna State Opera, or the Naschmarkt. If you have less time, skip the interior of the Schönbrunn Palace or choose one section of the Kunsthistorisches Museum to focus on. Don't forget to try the local cuisine, such as schnitzel and Sachertorte, and take a stroll through the historic center of Vienna, which is a UNESCO World Heritage Site.