Well the answers so far have shown that those that replied probably know more about flying than astronomy.
The Sun and Moon are not connected in any way. So their periods are dissimilar. The moon orbits at about 25 hours, so its setting time can be at any time of day or night, and it always rises in the East and sets in the West.
The question asks where the greatest visibility will be.. obviously the area that the Moon is still shining upon, which will be to the West.
One interesting fact is that the Moon creates two High Tides per day, separated by 12 hours 25 minutes.