The speaker is a guy in New York who is standing with a view of the Brooklyn Bridge and musing on it. At one point he positions himself "across the harbor" from the bridge. At another point he describes waiting "by the piers." So this is clearly someone who knows the bridge, and the city, very well.
The speaker is fond of puns. Puns, wordplay, and little jokes are everywhere in the poem, like when he uses "sails" (like on a boat) to also mean "sales" (as in sales figures). He also likes using really archaic speech and old words that few people (even in 1930) would use in normal speech: "Thee," "inviolate," "parapets," "unfractioned," and the like. He kind of reminds us of the singer from the band The Decemberists. (If you've heard the band and its love of words like "palanquin," you know what we mean.) In short, this is a guy who would probably ace the New York Times crossword puzzle every day. In more academic terms, he's read his British Romantics and a healthy dose of Shakespeare.
The speaker has also clearly read the 19th century American poet Walt Whitman, because this poem has obvious similarities with Whitman's "Crossing Brooklyn Ferry." Like Whitman, he is interested in bringing diverse people together, and he has a fundamentally optimistic worldview. He can be cynical at times, though. For example, from the way he describes the movies in Stanza 3, you'd think that going to see a film would turn you into a mechanical droid.
Finally, the speaker is quite familiar with the dark side, or underbelly, of the city: its deranged, poor, and marginalized. Hart Crane's biography suggests at least two reasons why this might be. First, Crane was an alcoholic. Second, he was gay at a time that wasn't accepted. The speaker doesn't come out and yell, "Hey, I'm gay!" but his description of marginalized people makes us think this poem is fairly autobiographical.