In a
castle,
keep, or other such
establishment, the
Throne Room is where the
throne is, and thus where you're most likely to find the
monarch during
business hours.
In NetHack, there is a one-in-six chance on each level after 5 in the Dungeons of Doom that a throne room will exist on the level. If there is, you'll know very shortly, because throne rooms emit unmistakable ambient messages, like "You hear the tones of courtly conversation" and "Someone shouts, 'Off with her head!'".
A throne room will contain a throne and a chest. The room is filled with sleeping monsters of classes koCDGHT and possibly bugbears; the exact monsters vary according to how deep in the Dungeons you are. Sitting on the throne can produce interesting effects and is much safer than quaffing from fountains (see).