Imperial Palace (Hofburg)
The House of Habsburg was one of the most important royal dynasties in Europe and ruled Austria for six centuries. Through prudent marriages they managed to also gain Spain, Hungary, parts of France and many other lands. They built many fine churches and residences and rarely finished any of them. The Hofburg was the Imperial Palace until 1918, although strictly the Habsburg dynasty had died out and been succeeded by another by then. The palace remains the center of government for Austria but these days the occupier is a democratic republic rather than kings and queens.
The palace is an amalgam of eras and styles, much of it rich 17th and 18th century Baroque. Don't miss the Renaissance wing Stallburg where the famous dancing horse, the Lipizzaners, are stabled.
The closest metro station is Herrengasse on line U3. Or tram 1, 2, D and J, get off at stop Burgring. Buses 2A and 3A stop at Hofburg.