You just about have your answer right in the question. The short
answer is that moving eastward seems to relate to exile, while
moving westward is a return to the garden and the presence of
God. The long answer: The garden is planted in the east of Eden
The garden is the primeval meeting place between God and man. It
is the first sanctuary, where man is placed to work (serve) and
keep (guard) (Gen 2:15). These are the same tasks of the priests
and Levites with regard to the tabernacle (cf. Num 18:1-7).
Cherubim are stationed on the east side of the Garden of Eden
When Adam and Eve are exiled from the presence of God and from
access to the tree of life, they are sent out eastward. To re-
enter the garden, they would have to travel west and pass the
cherubim and flaming sword. Also, after Cain murders his
brother, he is driven even further east, further from the
garden. By implication, the cherubim are also guarding the way
into Eden itself, which is higher up and further west than the
garden. I'll come back to