The episode is divided between the present day (or thereabouts) and 1938. In 1938, the Weeping Angels have stealthily taken over Manhattan. They trap people in an apartment building of which they seem to be the landlords, and feed off their temporal energy. They're so terrifying that even a crime boss named Grayles is freaked right out and hires a private detective to investigate them. The detective ends up getting trapped in the apartment building, where he comes face to face with his older self. Every time someone tries to escape the building, they get zapped back in time and eventually die of old age. Also, somehow, the Statue of Liberty is a Weeping Angel and she's managed to walk all the way across Upper New York Bay to the apartment building without anybody noticing.
In the present day (or thereabouts), the Doctor, Amy and Rory are visiting Manhattan. You know everything's worked out in the past, more or less, because Lady Liberty isn't still roaming the streets. The Doctor is reading a pulp novel about a detective named Melody Malone when he starts to realize that events in the book are describing events they're experiencing. This is because Melody Malone is Melody Pond, aka River Song. When the Angels zap Rory back to 1938, the Doctor and Amy use the book to figure out what they're supposed to do. This is all well and good until the Doctor realizes some bad stuff is coming and doesn't want to read too far ahead.
For some reason, that terrified crime boss is collecting angels in his mansion. This is where River and Rory end up, and where the Doctor and Amy eventually find them. After escaping Grayles's Angel collection, Rory is trapped in the apartment building from hell, where, like the detective from earlier, he sees his older self. When the rest of the crew catch up to him, they decide that the only way to escape the Angels is to create a paradox that will poison them. Rory and Amy throw themselves off the top of the building to their deaths, thus preventing his older self from ever getting trapped there. They come back to life (paradox!) in a cemetery and everything seems fine and happy and like everybody's cheated their fates.
That's when an Angel shows up to zap Rory back to the past. Because of all the wonky time shenanigans, they can't just TARDIS themselves over to save him, so Amy decides to give herself over to the Angel in the hopes that she'll end up in the same place and time as her husband. Luckily, it works, and we know so because both their names appear on a headstone in the cemetery. An afterword from Amy in Melody Malone's book lets us know that the Williams-Pond pair lived a long life together in the past. The Doctor is devastated, but vows to keep traveling. Stay tuned for the full weecap.
Someone taps away at an old-fashioned typewriter as a man with an American accent narrates. "New York. City of a million stories. Half of them are true. The other half just haven't happened yet." What is with the framing devices this season? Was there a sale at Cliché Depot? It's a woman's hands doing the typing, but a guy doing the talking. Does this guy even exist or is he merely a construct of the as-yet-unknown author so she can set up the story? The male narrator is a private investigator named Garner. He's been contacted by a Mr. Grayle regarding some statues that come to life in the dark. Garner doesn't really believe his new client, but he'll take the case for a whopping $25 a day. As if it weren't already obvious from the typewriter, we are in the Olden Days. He heads out into the rain with his riches. As he passes by a pair of statues, one of them vanishes.
Garner heads off to an apartment building where the statues supposedly live. Our lady author types and Garner narrates. "Grayle was the scariest guy I knew. If something scared him, I kinda wanted to shake its hand." I won't mention every instance of the appearance of statues in this episode, but they're everywhere. They're poised as gargoyles, perched in parks, holding up urns in fountains. The building doors open as Garner approaches. Inside, the elevator doors open as if anticipating him. He's creeped out, but gets inside. Upstairs, he comes to a door marked with his own name. When he looks around inside, he finds an ID card identical to the one in his own wallet. An old man beckons to him from his bedroom. "They're coming for you. They're going to send you back," he says. "Who's coming? Back where?" Garner asks. "Back in time," the old man says. "I'm you," he goes on. "I'm you!" With that, the old version of Garner dies.
Young Garner tries to get the hell away, but the hallway is suddenly blocked off by Weeping Angels. He tries the stairs and finds the route down blocked, as well. He makes a run for the rooftop. The earth shakes a few times. "You gotta be kidding me," Garner says, finding himself face to face with the snarling rictus of the Statue of Liberty. As per the rules previously established by this show, she somehow got from Liberty Island to Battery Park without anybody looking at (and thus immobilizing) her. The lady author types a chapter title at the top of the page: "The Dying Detective." Cue opening credits.
We return to the present day. "I'm an alien, I'm a legal alien," Sting sings. "I'm an Englishman in New York." I'm not saying it's on the nose, or anything, but it's hanging out somewhere around the nostril. Amy, Rory and the Doctor hang out in Central Park on a lovely sunny day. Amy tries to read the paper in silence, but the Doctor is annoying her by reading a pulp novel aloud: "New York growls at my window, but I was ready for it. My stocking seams were straight, my lipstick was combat ready and I was packing cleavage that could fell an ox at 20 feet." I haven't met many oxen, granted, but I feel like they probably don't care one way or the other about lady boobs. The Doctor, however, seems quite taken with this fictional private detective named Melody Malone, giving her description a "yowza!" of approval. "Only you could fancy someone in a book," Rory says. Um... what? The Doctor changes the subject by snitting about Amy's new reading glasses, which he thinks makes her eyes look wrinkly. He lifts them up to get a better look at her and realizes that, oops, it's not the glasses doing that. Also: Amy totally doesn't have wrinkles. Rory scampers away to get out of the conversation and get them all some coffee.