A slightly more detailed summary for "The King of Eden"
There's a summary in the programme, so I'll try to translate what I don't remember/didn't understand.
Saki finally figures out that Takizawa's message is referring to New York. Unfortunately, the other Selacao have also worked out where he is.
Saki flies over to New York with the support of all her friends (except possibly Ohsugi), and inadvertantly causes her taxi driver to drop her off at Grand Central Station. She lands in trouble when he discovers guns in her luggage, and rushes off with her handbag, with the Noblesse phone, still in the car.
Saki, who had picked up one of the handguns in her confusions, manages to make it to her hotel and call her friends (she has her purse on her), who start worrying intensely once they discover that No. 6 was the one who planted the guns. She, however, convinces them to let her visit a certain spot in New York.
She heads to the Brooklyn Bridge, from which you can see New York's Ground Zero (remember the one photo of Tokyo's Ground Zero that Takizawa took with Saki ? With the two lights pointing up at the sky?) Finding no sign of Takizawa, she takes out the gun and wonders what to do with it...and...
"What are you doing?"
Takizawa takes the gun from Saki and throws it into the river (the Hudson, I assume), before taking her hand and running off. He walks off, but..."Takizawa-kun!"
However, he now knows himself as Iinuma Akira...「俺、飯沼だけど？」
Saki falters...but tells him that she's in New York looking for someone, and that she's lost her purse. He decides to help her find it. Luckily for Saki, she still has the receipt from the driver.
On the way to the company's head of operations, Saki tells her companion more about the person she's looking for. "Actually, I've found him, but he doesn't remember me." "That's terrible!" LOL
Not knowing any English, Takizawa gets Saki's bag back by some admirable acting (I've leave you all to watch this for yourself). Having accomplished this, he is about to part ways, but she tells him that, in fact, the person she is looking for is him. At his puzzled look, she shows him the "ground zero" picture that they took together back in Tokyo. Takizawa then invites her back to his apartment for the time being.
Takizawa has been staying at the Gramercy Park Hotel for the past 6 months. He has no recollection of taking the room, but the key was in a bunch of keys that he found in Washington. Unfortunately...
No. 6 turns out to be some douche bag who is apparently trying to make a movie as part of his plan to save the world...he causes trouble for Saki because he figures that the prince will come to save 'the damsel in distress'.
Saki's friends realise that No. 6 has just ordered a malfunction in the heater in Takizawa's apartment, but they can't contact her.
However, the Noblesse phone rings, and No. 11's voice tells Takizawa to get away from the heater/get out of there. As the building explodes, No. 6 is surprised to see the two of them running away safely.
Takizawa takes Saki to the Angelica Film Center, where he works part time. (According to the programme, after the 60 missiles incident, the police released him suddenly and he was told to go to the cinema where he had seen "Dumbo". Incidentally, the cinema's walls are lined with the same posters at Takizawa's home complex in Tokyo...) They stay the night there in one of the theaters, though Takazawa stays by Saki's side this time.
Some time during the course of this day, Takizawa tells her that, for some reason, he had been compelled to go to the Brooklyn Bridge everyday. So, although he doesn't remember, he believes her story.
The following day, remembering the "golden ring" that Takizawa talked about on the cinema's rooftop back in Japan (programme), they make their way to a small amusement park with a merry-go-round. There, barely reachable from a pony on the ride, is a golden ring. (Programme: further evidence that he lived in New York before?)
Unfortunately, No. 6 interrupts their 'date' again by having the police come to accost the pair...and this time, No. 11 arrives to retrieve them and get Takizawa back to Japan...in order to meet his mother...
In the meantime, No. 1 takes advantage of the chaos caused by No. 6, and starts getting rid of the opposition. He orders some missile attacks, targeting the trailers that we saw leaving the scene at the end of episode 11. (He seems to have targeted the Juiz supercomputers of No. 12, No. 2 and No. 9 specifically because he feels that he may be able to obtain Juiz if they are not around.)
He also compromises the Eden of the East server, and seems to be working to erase all traces of Takizawa Akira's existence. (edit: actually, Juiz is responsible for this - as part and parcel of Takizawa's last request.)
No. 1 manages to destroy 2 and 12, which results in the respective Selecao being taken offline. His final target seems to be No. 9, but No. 11 moves her trailer up to take the missile instead. Thanks to Kuroha's sacrifice, Takizawa is still in the game. He and Saki head back to Japan...
No. 10 (Yuuki) turns up in front of No. 2 at the end of the film (after the trailers have been destroyed). It turns out that he broke his own Noblesse phone so as not to be tracked.