Technically, Yeats died in a hospital. We know this because, well, the first section spends a good bit of time talking about the mundane details of dying in a hospital. But that's really the boring part of this poem – and intentionally so. Auden's language makes it clear to us that death is often mundane and boring and, well, full of hospitals and other not-so-fun stuff.
But that's only the beginning. See, the imaginative scope of the poem takes in a whole lot more than just the setting of Yeats's actual death. It pans out to rove over the whole landscape of his life, including his deep love for his home country, Ireland. Remember the bit where the speaker announces that "Mad Ireland hurt" Yeats into poetry? OK, so the poem is not "set" in Ireland in the traditional sense. We don't get descriptions of rolling hills and leprechauns. But it is the emotional heart of the poem, which, in our book, is every bit as interesting.
Panning out even further, the setting expands to include the events that were going on in the world in 1939. Auden manages to paint a vivid picture of a world built of isolationists. (Hmm...sounds like the foreign-policy agenda of the US at the time.) Oh, and don't forget the nightmarish oncoming of World War II.
Combine all three settings and you've got a poem that can talk about the nitty-gritty, mundane details of life at the same time as it philosophizes on the state of world affairs. Pretty impressive, huh?