Idaho is so often defined by its borders with other states. In the Southeast, Idaho Falls is a gateway to Yellowstone and the Tetons which primarily lie in Wyoming. The southeastern part of the state is also culturally linked to Salt Lake City due to the I-15 corridor and the high mormon population. The Southwest shares the Owyhee Canyonlands with Nevada and Oregon, While the Northern Pandhandle Is connected by metro-population and biome to Washington and Montana.
Idaho is Pacific Northwest obviously in the north where large conifers abound, but also through the arid ecosystems of the Owyhees and Snake River Plain which greatly mirror Eastern Washington and Oregon. The Volcanic activity of the Cascade range is complimented by the volcanic activity of the Yellowstone Hotspot footprint and the Snake river drains much of Idaho which flows into the Columbia making Lewiston the farthest inland port on that river system.
Idaho is also Intermountain West. Many of its mountain chains continue on into Montana, Wyoming, and Utah. Much of the Eastern population is connected to other Intermountain cities, Like SLC or Jackson Hole; and some of Idaho's rivers drain into Utah.
Now I would argue Idaho is also the Southwest. When formulating regions, the settlement and relation of populations is important. Southern Idaho's indigenous people speak Uto-Aztecan languages which dominate the Southwest. The rock formation and erosion patterns of the Owyhees and the Snake River Canyon are complimentary to rock formations further south. The Snake River Plain is the northern part of the Great Basin Desert which stretches down past Southern Utah and Nevada.
I see the borders to regions of the United States not like official markers on a map or a line which indicates a beginning and an end. Maybe a better comparison would be fingers interlocked or ripples in a pond interacting with one another having areas of concentration as well as areas of very light influence. In my mind and through my experience there is no doubt; Idaho is Pacific Northwest, Intermountain West, and Southwest.