"We see New York, and sometimes, as Henry James asked us to, we “do it”—explore and conquer it—but what we see when we see it is so far unlike what we experience when we’re doing it that the difference itself can become a subject for art."
The question is about "do it". There shouldn't be any problem about the meaning, as it is explained in the following (explore and conquer). But it is very hard to say "do it" in a foreign language, as many foreign languages don't have a word that can mean so many different menaings in different contexts, as "do" in English can. I am hoping someone can offer some sort of paraphrase.
experience it; come to know it; learn about it