"Her name was Joy. Your name is Amelia. You will tell the Doctor... What he must know. And what he must never know."
I guess Amy knows what it's talking about, but anyway she forgets about that conversation immediately, left only -- and this is key -- with the burning desire to tell the Doctor something, and no idea why it's so important for her to tell the Doctor this thing.
Back in the Oval Office, the phone rings, and somehow they figure out where the call is coming from: The intersection of Jefferson, Adams and Hamilton streets. Because of course nobody is called Jefferson Adams Hamilton (River, helpfully: " Surnames of three of America's founding fathers. Lovely fellas, two of them fancied me"), clearly this was read off street signs where three streets intersect and not the, oh, bajillion other places those names just might appear together.
Kid: "It's here! The Space Man's here. It's gonna get me. It's gonna eat me!"
Everybody loads onto the TARDIS to go save the kid, cue "bigger on the inside" dinner-plate eyes from Canton, but the kid's gone. The Doctor gives a belabored explanation of the street-intersection deal, causing River to get all turned on because he's hot when he's clever, which is true, and the Doctor to joke that she looks like that all the time because he's hot all the time, also true, and Rory explains the TARDIS to still-tilted Canton.
The empty warehouse contains a phone that isn't connected, and they set up camp. Isn't this obviously a trap? "Let's see if anyone tries to kill us, and work backwards." They find a lot of stolen NASA tech. The Doctor points out that 1969 is hardly the time you'd go for really good space travel junk, but decides that it's because it's totally cool-looking. There's a cute moment where Amy tells the Doctor he's not a "cool" alien, just a regular alien, and the Doctor does all kinds of adorable stuff, and they go looking for the little girl.
Sidebar where River "somehow" figures out what Amy's thinking, which is the obvious thing any of them would be, and in fact are, thinking: "Neutralize the Impossible Astronaut in 1969 so it doesn't kill Doctor 1100 in 2011." Problem: Apparently that would be a paradox. Details: Forthcoming. Or not. Time: Can be rewritten. Or not.
There is a network of tunnels beneath the warehouse, and in fact beneath all of America, so River heads down there without further ado to figure some shit out: "Don't worry, I'm quite the screamer. Now there's a spoiler for you!" (River is talking about sex.) Upstairs, Canton worries if he was actually slipped a mickey at the top of the episode, but no. Rory decides to join River down there -- where she's having her own womb/spacetime tummy issues we won't be explaining or revisiting -- and where she immediately forgets having just discovered a whole clutch of Silence.