The day when I met the most powerful man

Almost 3 years ago, when I was visiting Washington DC, I had a curious experience while I was a tourist.
I remember that I and some partners were walking around the White House and we were looking for something to eat. Suddenly, before crossing one street, we noticed a lot of people joined together in the corner. I thought there might have been  had happed an accident, because there were some patrol cars. When we were arriving, in an instant I noticed what  was happening it's gonna happen:  The president of United States was arriving at home! First, I saw many police motorcycles going very fast, there were a lot of them!. Then, we were impressed when the two twin limousines arrived. Everyone started to shout and clap when a man looked out of a window of the second limousine, it was Mr. President Barack Obama.

Usualmente, nu usamos Mr. President Obama..  es Mr. President o President Obama.  President > Mr.

Igual con Dr.,    Nunca decimos Mr. Dr. Smith. 

The day when I met the most powerful man

Almost 3 years ago, when I was visiting Washington DC, I had a curiuos* an interesting or exciting experience while I was touristing. I remember that I and some patners  some partners and I ** were walking around the White House and we were*** looking for something to eat. Suddenly, before crossing one street, we noticed a lot of people joined hanging out  on in the corner. I thought it had happed  there was an accident, because there were some patrol cars. In an instant, when we were arriving, in a instant I noticed what it's was gonna happen: the president of United States was arriving at home! First, I saw many police motorcycles going too fast;, they there were a lot!. Then, Next, we were impressed when the two twins limousines arrived. Everyone started to shout and clap, when a hand looked out of a window of the second limousine, it was Mr. President Barack Obama (order of sentence matters in this case because it reads like the hand came first and then people started clapping...think about saying...When a hand looked out of a window in the second limousine, everyone started to shout and clap--it was President Barack Obama).

*curious makes me think of something that you are eager to learn something.  Exciting fits best in my opinion.

**you could say me and some partners (not I and some partners) but that the use of me is slang.  In proper English we refer to I second in a list of people doing something.

***since you have the verb we were at the beginning of the sentence you can leave it out here.  this makes the looking for something to eat a prepositional phrase like the next sentence you wrote.

****people aren't joined together except in marriage

use semicolon or period between to independent sentences; in the case of the last sentence you can also use a --(dash) or ... (ellipsis) to emphasize a main point of the sentence.

Very good job!