Yeats, who was born near Dublin, Ireland, grew up as a child in the rural district of Sligo, on Ireland's northwestern coast. When he wrote "The Lake Isle of Innisfree" in the 1880s, he and his family were living in poverty in England. It is written that the sound of a splashing fountain on a busy London street inspired the poem, reminding him of Ireland and the specific place where, as a boy, he had always wanted to live.
Thus, the setting of the poem was born of Yeats' childhood memories and creative imagination--a place of natural beauty far removed from an industrial city, a place where one could find peace. The specific details in the poem romanticize Innisfree as an escape from the complexities of modern life where one could live in simple harmony with the natural world.
I am not sure how precise it is possible to be when discussing the setting of this poem in terms of time and place.
In terms of place, it is presumably set in Ireland. I say this because there is a place called Innisfree in Ireland. Yeats had dreams of living there as a young boy so one may presume he is talking about it.
As far as time, there is nothing to indicate that they poem is set in any time other than the late 1880s when it was written. We do know that there are roads and that there are "pavements" -- probably cobblestones. That indicates that it is at least in modern times.
Escaping to a place where we feel less burdened has been a constant human reaction to stress or unhappiness. Thus, poets, who more often than not characterize their own emotions through their words, have a way of making even the description of this comfort seem magical. The poem, inspired by Thoreau’s Walden, seems to waver between engagement and disengagement. Is the poet trying to go somewhere, or is he trying to get away from everywhere?
Yeats’s lines provide rich rows of sounds to hoe: assonance (from I . . . arise in the first stanza through the o-sounds in the closing stanza), onomatopoeia (lapping), initial alliteration, internal alliteration (arise, Innisfree; hear, heart’s core). Sound images of bees, cricket, linnet, and lake water are predominate. Whatever noises come from roadway or pavement, however, are left unspecified.
If he will go, will it be in the future? And, does he want the noisy solitude of rural life as opposed to a stark urban life?