Both the Vilna Gaon and Malbim write that the verse mentions so many locations because Esther stood outside his private residence, where Achashverosh was expected to be. H-Shem had arranged it so that Achashverosh was then in court, able to see Esther outside his residence. This way, she was suddenly in the public courtyard, and he felt unable to order her execution. Like the reasons he had to give him pause before having Vashti killed, the king again did not want to appear insecure, especially since this would be the second wife he’d have executed.
As the Alshich points out, since Esther was right in front of Achashverosh, nobody would be able to attack her without his say-so.
Finally, the Imrei Emes, in a less literal interpretation of the verse, writes that the verse’s description of Esther’s location is a spiritual dimension. This is not a physical courtyard. Rather, the added power of Esther’s accomplished Ruach HaKodesh, her powerful prayer, and her self-sacrifice transported Esther into H-Shem’s Inner Courtyard, where He made Himself more receptive to her plea.