The expressions in the text indicate the position which she takes and its capabilities. At the hand of the gates (1 Samuel 19:3). She posts herself at the side of the city gates, under the archway pierced in the wall, where she is sure of an audience.
At the mouth of the city, inside the gate, where people pass on their way to the country. At the coming in at the doors, by which persons enter the town. Thus she catches all comers, those who are entering, as well as those who are leaving the city.
Here standing, as in the Agora or Forum, she crieth; she calls aloud, saying what follows (Proverbs 8:4-36). It is a fine picture of the comprehensiveness of the gospel, which is meant for high and low, prince and peasant; which is proclaimed everywhere, in the courts of kings, in the lanes of the country, in the hovels of the city; which sets forth the infinite love of God, who is not willing that any should perish, but would have all men come to the knowledge of the truth (2 Peter 3:9).
Septuagint, "By the gates of the mighty she sits, in the entrances she sings aloud ( ὑμνεῖται)."