If you want to explore the city further, especially its art or music history by visiting more specialized museums and taking part in an opera soirée, then add another 2 days to that, making it 5 fantastic days in Vienna!
The most important sights include the Staphansdom and city center, the state library, the Hofburg palace, the Schönbrunn Palace, the Opera, the twin art history and nature history museums and the Prater with the giant ferries's wheel.