At what time of the day is the moon closest to earth?
The distance from the Earth to the Moon doesn't vary very much over the course of a day and it depends on where the Moon is in its orbit.
The Moon orbits the Earth in what approximates to an elliptic orbit. The actual shape of the Moon's orbit changes continuously due to very complex gravitational effects which won't be described here.
The Moon's is at its closest to the Earth when it is at perigee and at its furthest when it is at apogee. The time between consecutive perigees is called the anomalistic month which is approximately 27.55455 days.
So, the Moon is closest to Earth at the start of the day if it the Moon is between perigee and apogee. It will be closest at the end of the day if it is between apogee and perigee. It the day is the day of perigee the Moon will be closest at the moment of perigee.
If perigee coincides with a full moon we get a super moon where the Moon appears at its largest.