The title of the poem gives us the where, but it's crucial also to understand that "America" is set firmly in the 1950s. In the years just after World War II, America underwent an economic surge (not just babies were booming) and rushed headlong into a world of suburban tract homes, gray flannel suits, and shiny new refrigerators. Just pop on an episode of Leave it to Beaver to get a sense of how the media in the 1950s encouraged Americans to live their lives.
Of course, this fantasy—white picket fence, stay-at-home mom, working dad, two kids, and a dog—was in many ways just that: a fantasy. African Americans, homosexuals, immigrants, and many others were written out of the American dream script entirely. As well, all the good feelings between America and Russia in World War II started to harden into the Cold War, as either side rushed to out-build the other's nuclear arsenal.
This kind of mindset is precisely what the speaker is arguing against when he asks, "when will we end the human war?" (4) and then confesses that America's "machinery it too much for [him] (17). The militarism and pressure to conform to a narrow set of ideals is what drives the speaker's complaints in the poem, and why he is in search of a better way of living, both for himself and his country.
So, Ginsberg's "America" is reacting to a very different place that the one you might see the Beav in. Between the stresses of conformity and materialism, the threat of nuclear war, and the social oppression of minority groups, we can start to understand just why the speaker says, "I don't feel good don't bother me" (6).