Why? Because only there you can admire the crown of the emperors of the Holy Roman Empire or the Agate bowl that was belived to be the Holy Grail.
If you like "treasures", emporerstories, invaluable relicts and items, you really have to go there.
With over 1000 years worth of Royal treasury items the Imperial Treasury (Schatzkammer) at the Hofburg Palace is regarded as one of the most important in the world.
“Modeled on St. Peter's in Rome, the Collegial and Parish Church of St. Peter (Peterskirche) is built on a site originally occupied by a Roman church and later by one founded by Charlemagne in 792 AD. The present edifice was built in the 18th century and boasts a massive dome with a superb fresco and many artistic treasures. Other highlights include the Barbara Chapel with its magnificent portal, and in which Franz Karl Remp's Decollation of St. Barbara is found, and the choir with its High Altar and painting of the Immaculate Conception. Also of note is the nearby Plague Pillar, a 21-meter-tall Baroque pillar built to commemorate the end of the devastating plague of 1679 that cost at least 75,000 Viennese their lives. Also of interest is the nearby Abbey of the Scots (Schottenstift), built in the 12th century and extensively renovated and enlarged since. Its school included Johann Strauss and Austria's last emperor, Charles I, among its pupils, while its fine collection of artwork includes pieces from the 16th to 19th centuries.”
“Platz zwischen den Museen, atemberaubende Gebäude. Im Winter ist hier ein Christkindlmarkt.”
“This former insane asylum now holds a pathological anatomy museum. Meaning “Fools’ Tower,” the Narrenturm was one of the first insane asylums ever built. Today the Narrenturm no longer holds mentally imbalanced Viennese, but it does contain something else of interest: The Anatomical-Pathological Museum. While the circular building (known by locals as “the poundcake”) houses only a small percent of the museum’s total collection, it contains some fascinating pieces. Syphilitic skulls that resemble Swiss cheese, jars of disfigured fetuses, and graphic wax displays of untreated STDs all peer out at you from the old cells. It also contains a recreated wonder cabinet, complete with a narwhal tusk and taxidermied monkeys. Keep your eyes open for the Hydrocephalic skeleton, towards the end of the museum. His enormous head is hard to miss. Update August 2017: The building is undergoing a major renovation and much of the collection has been moved into storage. ”