Where does the moon go each morning?

Moon doesn't go anywhere during the day. It keeps on orbiting the earth as usual. We normally see the moon during night because Sun's bright light doesn't allow us to see fainter objects.

However, moon is an exception to that because moon is a very big astronomical body and very close to earth. If the conditions are right you can see the moon during daytime as well.

"Sometimes to see the moon you'd have to look through the Earth and we can't do that,"

"When we see the moon during the day it's because the moon is in the right spot in the sky and it's reflecting enough light to be as bright, or brighter, than the sky."

The moon continues on its orbit around our earth regardless of the day-night cycle on earth. When the moon is full it pretty much rises as the sunsets and sets when the sun rises. However when the moon is a New Moon it sets just after the Sun. And will be mostly visible if you look for it in the daytime sky. The moon just like the earth has 50% of its surface in the sunlight at any given moment with the exception of lunar eclipses when earth blocks the sun from striking the moon. So the moon is visible in the daytime on earth just as much as it is at night time on earth.