In Batman: Arkham Origins, Batman first meets the Joker at the Gotham Royal Hotel, commonly shortened to the Royal Hotel.
Batman tracks an electromagnetic signal associated with the Electrocutioner's gloves to the hotel on Christmas Eve. The building has been seized by Joker's gang, rigged with explosives, and transformed into a grotesque “house of horrors” filled with traps and hostage situations.
The encounter is a turning point in the prequel's story. Batman initially believes he is pursuing Black Mask, but the hotel sequence exposes the criminal's real identity and begins the Joker's fixation on Batman. Bane is also central to the confrontation, including a major battle that tests the still-inexperienced Dark Knight.
The hotel is sometimes called Gotham Royal Hotel in descriptions and walkthroughs, while the game and fan references often shorten it to Royal Hotel. That wording difference does not change the location. It should not be confused with a generic Gotham Hotel or a separate penthouse location inside the building.