The Imperial Treasury holds the crown of the Holy Roman Empire, eight gold plates hinged together into a rough octagon. It sits in low vaulted rooms off the Schweizerhof, the oldest courtyard of the Hofburg, where there is no daylight at all. The rooms are kept dim and only the cases are lit, so the gold shows up from across the room. Almost everything is small and behind glass, so you look at close range.
The empire elected its rulers and had no capital, so the crown never had a home. It travelled instead, and for most of four centuries it lay locked away in Nuremberg, coming out only when somebody was being crowned. It was carried east in 1796 ahead of the French armies and reached Vienna in 1800; six years later the empire was dissolved and it simply stayed. The Habsburgs kept their own treasure in these same rooms, including the robes of the Order of the Golden Fleece, inherited from the dukes of Burgundy. Look for the late Roman agate bowl: it was long taken for the Holy Grail.