All the creativity seemingly went into the architecture, rather than the name: Hof means court and Graben is the name of the street outside.
It’s easily spotted thanks to its location opposite the plague column. It also has the word “Grabenhof” written helpfully in large letters on its facade. You can see some photos within this slideshow of buildings designed by Otto Wagner (for me, the decorated golden railings are the highlight):
The first constructions on the site date back to at least the 14th century. Sometime in the late 16th century, the owners put up the Renaissance Arkadenhaus. This was, in turn, replaced by the Grabenhof, finished in 1876 and designed by Wagner and Otto Thienemann. There’s another Wagner design just a few steps away: the Ankerhaus at Number 10.
The site is replete with history. For example, it’s been a bargaining chip for monasteries and dukes, provided holding cells for 16th-century courts, and housed the company that published Schubert’s music.
In 1804, they formally announced Francis I’s new title of Emperor of Austria from one of the balconies. This is less impressive than it sounds since he unilaterally declared himself Emperor of Austria, fearing (accurately as it turns out) that his existing title of Holy Roman Emperor would soon be made redundant by Napoleon’s European adventures.
Even the newer Grabenhof enjoyed its own brushes with history. It temporarily housed offices of the Third Reich, for example. In WWII, it was damaged by aerial bombing and during the land battle for Vienna. Upmarket stores (e.g. Longchamp and Mont Blanc at the time of writing) now fill the street-facing ground floor.
HOW TO GET TO GRABENHOF
It’s hard to miss, being on one of the main tourist walking routes through the historic center of Vienna.
Subway: Wander up the Graben from the Stephansplatz station (on the U1 and U3 lines)
Bus: Lines 1A or 2A to Graben/Petersplatz
Address: Graben 14/15, 1010 Vienna
Map of Otto Wagner buildings and landmarks: