In general, the setting is a cross between modern-day Ireland and the ancient Greece of epic stories like Homer's Iliad. But trying to figure out the setting of this poem is a bit like playing that Halloween game where someone blindfolds you, places different foods in front you, and says, "These are eyes! These are brains!" Except instead of foods, Yeats places "symbols" in front of the reader. That's why Yeats is often described as a Symbolist poet.
On the whole, the setting is vague, general, and driven more by ideas than specific images. As readers we're blindfolded. Yeats puts the "little streets" in front of us and says, "This represents the working class in Ireland," and we're like, "Sure, why not?" He puts a "tightened bow" in our hands and says, "This represents an ancient Greek ideal of beauty that is both graceful and powerful," and we're like, "Makes sense." And so on.
"No Second Troy" is not the kind of poem where you're going to hear a lot about babbling brooks and whispering winds. And we're fine with that, because the few images we are given have been chosen very carefully to place us at the intersection of ancient nobility and modern instability.