In the poem "Out Where The West Begins" the West is a state of mind.
For the Northern states I've always thought of it as starting West of Billings and running to the top of the Cascades. Anything further West is the Pacific Northwest and places to the East are either part of the middle of nowhere (big parts of Eastern Montana) or the Midwest - although Western ND might be part of the West. The West probably encompasses parts of Wyoming, Colorado, Utah, Idaho, Arizona, Eastern Oregon and California. Not sure about New Mexico I haven't been there enough to get a feel.
Purely subjective on my part.