It is 12:20 in New York a Friday three days after Bastille day, yes
The poem begins like a police report, with the time and date.
The speaker drops the setting in our lap and says, "Here's the setting. This is when and where the poem is set." Thanks, Frank.
O'Hara wrote this poem on his lunch break, and it's already 12:20pm, so the speaker is narrating the time literally right before the poem was written. It's Friday, so he might be looking forward to the weekend and not too worried about getting back to work immediately.
The speaker provides the date in an off-hand manner: it's three days after Bastille Day.
Being total Francophiles, we know that Bastille Day is like the French version of Independence Day. It celebrates the liberation of the Bastille prison in Paris in 1789, a pivotal event at the beginning of the French Revolution.
We learn two things from the casual mention of Bastille Day. First, it must be July 17, because Bastille Day is always July 14. Second, our speaker seems to be a hip intellectual type, since he's keeping track of French holidays.
The last word of line two is "yes." It's as if the speaker is thinking fast and going back to review what he just said. "Is that right? Three days? Yes."
It also sounds like a flashy celebrity news reporter trying to drum up excitement. "We're here outside Mann's Chinese Theater in Los Angeles, and, yes, the stars have come out tonight!"
it is 1959 and I go get a shoeshine because I will get off the 4:19 in Easthampton at 7:15 and then go straight to dinner
Line 3 has something resembling traditional poetry, an internal rhyme.
Nonetheless, everything else about these lines is completely unconventional. Why? Because it's so darned conventional.
The speaker says he's going to get a shoeshine because he wants to look good when he meets his swanky friends in "Easthampton," by which he means "East Hampton," but he's talking so fast he crunches the name into one word.
As a favor to potential O'Hara stalkers across the world, he even provides the train schedule. Departure from New York City: 4:19pm Arrival in East Hampton: 7:15pm.
East Hampton is a very wealthy area of Long Island. Currently, a lot of celebrities have houses there, including Jerry Seinfeld and Martha Stewart. Even back in the late 50s, it was the kind of place where you'd better show up with your shoes polished to avoid having people look at you funny.
Biographical side note: Not only did O'Hara take the 4:19 train after writing this poem, but when he arrived in East Hampton, his friend was waiting for him with "a thermos of martinis" (source)!
Martinis from a thermos? Wow. The speaker's super-cool social status is an important part of this poem.
at 7:15 and then go straight to dinner and I don't know the people who will feed me
The speaker continues to plot out the rest of his day.
Remember that, except for the shoeshine, none of this has happened yet.
When he gets off the train, it's straight to dinner, except he doesn't know where yet.
The speaker sounds like a highly sought after person, maybe because he's an artist; so he gets free meals and housing pretty much whenever he wants.