We're gonna go ahead and say this poem takes place in a bedroom somewhere—you know, pillows, a bed, "a chamber deaf to noise"? It sure sounds like somebody's sleeping quarters to us, and not just any old sleeping quarters. They sound pretty primo, as in: the ideal place you would want to turn in for the night. We like to imagine this bed as one of those cool ones with curtains all around it so you can completely shut out all light and feel like you have some privacy, just like this.
But there's more to the setting of this poem than just an awesome four-post bed. The speaker talks a lot about his feelings and emotions ("civil wars in me," "weary head") and implicitly encourages us to get inside his head a little bit. While this isn't one of those brooding, emo poems, a good part of what happens in "Come Sleep! O Sleep" takes place in the speaker's heart, so to speak, the battleground of emotion.
The last thing to consider relative to setting is the world of the Renaissance sonnet. Okay okay, this isn't a real place, but it is a literary landscape that you should know a little bit about. Lots of sonnets from the period are littered with stories of unrequited love, dreams about one's beloved, outlandish and hyperbolic claims about the beloved's beauty, and, of course, sleep. While this poem evokes some of these, the whole sequence (Astrophel and Stella) evokes all of them. The point to keep in mind, then, is that while this poem literally takes place in a bedroom, it also part of the larger world or context of Renaissance love poetry and sonnet sequences.