The overarching setting is in the mind of the narrator Prufrock. He is reflecting on his past experiences and thinking hypothetically about alternative futures. Basically, he is a middle-aged man with a degree of social anxiety thinking about how his shyness and indecision have caused him to miss out on romance. What might make the poem less confusing to you is to imagine it as a sort of daydream in which the narrator is perhaps bored or sleepy and is just letting his mind drift. It is not intended to be a coherent narrative, but just a series of reflections and impressions about events that have occurred, that might occur in the future, or pure fantasies.
One important setting is the streets of London. This makes the poem a typical work of modernism in having urban settings and themes. Instead of following earlier traditions of love being seen in pastoral environments or the stable social structure of the village or small town, the backdrop of Prufrock's lack of ability to connect romantically is the vast anonymity of the city and lack of cohesive social bonds in a society no longer held together by institutions such as the Church or stable communities.
A second major setting is the fashionable urban drawing room of the upper middle classes. This is Prufrock's social environment and the one in which he encounters women. In this environment, status is important and the narrator is hyper-aware of status markers and subtle cues in social interactions. Fear of getting these subtle social cues wrong leads him to anxiety and paralysis.
A third setting is a beach. This is a fantasy environment rather than a realistic one. First, one imagines the narrator walking on a beach, but as the narrator does so, he begins to daydream about mermaids and an underwater fantastical setting of "the chambers of the sea."