"Out west" and "back east" are holdovers from the days when the U.S. pretty much consisted of territory along the Atlantic seaboard. Then came westward expansion/Manifest Destiny etc. Lewis and Clark went "out"; and then they came "back". Get it?
An interesting and little known variation on this semantical theme is that "the
Northwest" originally encompassed what would become the states of Ohio, Indiana, Illinois, Michigan, and Wisconsin, as well as the northeastern part of Minnesota.
Map of "the Northwest" in 1787 That's why, once we settled a small kerfuffle with Canada as to who actually owned/controlled what was then known as the Oregon Territory, that whole area became known as "The
Pacific Northwest.