Jacob's well was there. Jesus therefore, being tired from his journey, sat down by the well. It was about the sixth hour{noon}.
To this writer, it seems that the extensive results that flowed out of this episode, such as the coming of the whole city out to meet Jesus, and their inviting him and his disciples to stay with them, indicate that the event happened at noon.  Of weight in this preference is the fact of the woman's having come to the well alone, rather than with a group of women who, like herself, needed water.  It is written of Abraham's servant that "He made his camels kneel down without the city by a well of water at the time of the evening, even the time that women go out to draw water"  (Genesis 24:11). Now, if the woman had gone to the well at the usual time, there is the probability of the presence of others and the absence of the privacy evident in this narrative.  Also, the social status of the woman suggests that she might have preferred to go at a time when she would not have encountered the neighbors.