When David first leaves Brooklyn, he says,
Perhaps, as we say in America, I wanted to find myself. This is an interesting phrase, not current as far as I know in the language of any other people, which certainly does not mean what it says but betrays a nagging suspicion that something has been misplaced. I think now that if I had any intimation that the self I was going to find would turn out to be only the same self from which I had spent so much time in flight, I would have stayed at home. (1.1.76)
What is key here is that David's sense of self is bound up with the fact that he is an American. He claims, half in jest, that he left America because he was searching for himself. Of course, the search for self is not a physical one and might as easily have been conducted alone in his room in Brooklyn. Yet David feels the need to move, to physically enact his mental search, even if he suspects that he is not so much searching for himself as attempting to lose himself.
The latter possibility, that David is actually in flight, is something that often gets left out of soul-searching narratives. Americans are famously (and, in Europe, notoriously) known for their optimism, their sense that everything will work out in the end, that history is moving forward in one progressive direction.
In their first conversation, Giovanni mocks this American ideal. David says that, in contrast to Paris, in New York, you feel "all the time to come" (1.2.92). Giovanni seems to regard American optimism as twinned with naïveté, as a result of the fact that it is a young nation. He jokes about how time sounds like "a triumphant parade" for Americans, and they think that with enough time, "everything will be settled, solved, put in its place." Then, in a scathing indictment of America, Giovanni says, "And when I say everything, I mean all the serious, dreadful things, like pain and death and love, in which you Americans do not believe" (1.2.101). It's not lost on the keen reader that this accusation closely resembles the one that Giovanni later makes when David leaves him; his ideas about America and his ideas about David are intertwined.
There is some difference between Europe and America that Giovanni has hit on, even if he has exaggerated it. For one thing, Europe has a much longer history than modern America. Of course, America also has a history that begins well before 1492, but the textbooks are just a wee bit biased. Yet this bias affects the way that we think, and in relation to European nations, America is quite young.
It is also an isolated nation, and neither Canada nor Mexico has posed a significant military threat for a long time. As recently as 60 years ago (and, in the book, ten years ago), Europe found itself ravaged by the most destructive war in world history. And the war unfolded in major European cities and on a European landscape. As awful as the World Wars were for Americans, imagine how much worse they would have been if battles were waged in the fields of Ohio and Arkansas, if cities like New York and Philadelphia were taken captive.
It's for these reasons that an Italian like Giovanni might think that Americans are naïve, that they are optimistic only because they can afford to be, because they don't know what it's like to have their nation taken over by a fascist leader. Yet the national talk is also extremely personal. When Giovanni makes comments about America, he is also, indirectly, making comments about David. When David responds and defends America, he is also defending himself.
The vision of America presented in the book, then, is one that is bound up in David and Giovanni's relationship. For David, America is the place of his youth, the place of people he loves and understands. Yet he would not have left it if he thought that his identity was not something else too, that he was not completely hemmed in by the fact that he was an American. As David says when Giovanni coyly refers to his nationality:
I resented being called an American (and resented resenting it) because it seemed to make me nothing more than that, whatever that was; and I resented being called not an American because it seemed to make me nothing. (2.2.12)
America, like his sexuality, is the identity from which David flees and yet he can't help the fact that it is an identity that defines him. Giovanni perceives this, but he picks on David because he thinks that David, like his nation, is young and naïve and inexperienced. When we learn about Giovanni's horrific past in Italy, we begin to understand why he can't take things quite so lightly as David does.
As Giovanni says quite succinctly, "The Americans have no sense of doom, none whatever" (2.2.218). America, then, functions not just as a physical place but also as a symbol of youth and innocence and naïveté, of a past from which David wants to escape and to which he longs to return.