Photo: Von Manfred Morgner Manfred Morgner, CC BY-SA 2.5 via Wikimedia Commons
This magnificent historic library was designed by Johann Bernhard Fischer von Erlach and built in 1726. As well as the spectacular room itself, you can see temporary exhibitions on various historical subjects.
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Fantastic Realism Museum
An unusual museum dedicated to the work of the Vienna School of Fantastic Realism (Wiener Schule des Phantastischen Realismus), highlighting works by artists Ernst Fuchs, Arik Brauer, Rudolf Hausner, Wolfgang Hutter and Fritz Janschka. An extra section of the museum displays paintings by international artists, and the first floor is devoted to rotating special exhibits.
Loretokapelle / Hearts Crypt, Augustinian Church
Yet another example of the gruesome divide-and-conquer burial strategy of the Habsburg dynasty. It is said that other dynasties waged countless wars to acquire new lands, but "you, happy Austria, marry". Even in death, the Habsburgs placated three different churches with the honor of caring for their remains. The best known, the Kapuzinergruft, contains their actual bodies. St Stephens holds their innards (intestines and other parts taken out during the preservation process). But the Augustinerkirche holds, in the Herzgruft (Heart Crypt), all the Habsburgs' hearts. The tradition began in 1627 with Emperor Ferdinand IV, who wanted to "lay his heart at the feet of the Mother of God", literally. His heart, and those of his descendants, are preserved in silver jars which are carefully cared for by the Augustinian friars who run the church. When the renovation was underway it was found that the preservative in some of the caskets had evaporated over the years, leaving nothing but a dried-out, mummified heart.
Butterfly House
A tropical greenhouse with an amazing collection of live butterflies, will delight both children and adults.
Imperial Treasury; aka the Secular and Ecclesiastical Treasures
The best part of the Hofburg and an absolute must. It contains the Habsburgs' collection of jewels, crowns, and other valuables, perhaps the best on the Continent. Second only to a tour of the Kunsthistorisches Museum, of which the Schatzkammer is a part. There are 20 rooms of priceless treasures that give a fairly accurate representation of the ceremonial Habsburg court life over the centuries.
Chapel of the Imperial Palace
The original chapel of the Palace, built in Gothic style 1447-1449, was made over in Baroque style. On Sundays and Catholic holidays (of which the Austrians celebrate many), the Court Musicians perform here. This group is made up of members from the Vienna Boys Choir, as well as performers from the orchestra and choir of the Vienna State Opera. Tickets can be purchased online here.
Austrian Theater Museum
Housed in the Baroque Lobkowitz Palace, this museum displays stage models, costumes, and props, with special temporary exhibits.