Vienna has an efficient public transportation system that includes buses, trams, and metros. Consider buying a 72-hour Vienna Card, which gives you unlimited access to public transport and discounts on many attractions. A 3-day Vienna Card costs €21.90 and can be purchased at the airport or any information booth.
Travel time between attractions varies, but expect to spend around 20-30 minutes on average.
If you have more time, consider visiting the Hundertwasserhaus, a colorful apartment building designed by artist Friedensreich Hundertwasser, or taking a Danube river cruise. If you have less time, prioritize the three imperial palaces (Hofburg, Belvedere, and Schönbrunn) and the Old Town.