Due to the attraction of our moon (and Sun) our oceans undergo an up and down movement every day. So the water rises or falls by a couple of meters. But does this type of effect also occur with our atmosphere?
Yes, they are called atmospheric tides. They can be caused by the gravitational effect of the moon on the atmosphere (lunar tides) and also differential solar heating (thermal tides). I believe you are asking about the former which is much weaker than the latter.
You can find more about it here: https://www.springer.com/us/book/9789027726308 and https://physics.stackexchange.com/questions/201973/are-there-tides-in-the-atmosphere
The moon has the same effect on every part of our lovely(I think). The effect is much more clear to see on the ocean because water is less subtle than air-we see the water and see right through the air. The moon also has the same effect on the land and we don't even notice.