hall is cognate to Halle I think. The proper standard German translation for hall might be Gutshof. But primarily, Hof refers to a yard, and then derived from that, are related meanings. It can refer to a farm (in many German regions a farm consists of several houses /stables arranged in a way that the buildings form the enclosure of a yard, "der Hof", see also David Hasselhof: Hassel-Hof, the Farm of Hassel).

A rural hotel/Restaurant is sometimes referred to as a Gasthof (Gast=Guest).

court of justice = Gerichtshof

royal court = Königshof

atrium = Vorhof

The Korean word your referencing seems to stem from Hofbräu, which refers to the royal court, Hofbräu is the Bräu (= brew) with the royal warrant (from the Königs-Hof).