My second question would be, “How do they keep their prisoners alive for fifty or sixty years without ever letting them leave the hotel room?” I ask this question only so that I can answer it by depicting the hotel kitchen, entirely staffed by Weeping Angels who pay very close attention only to their own work. When you walk into the room, you see Weeping Angels with knives, Weeping Angels holding pots of boiling water, and one very unfortunate Weeping Angel who was in the midst of tossing pizza dough when you came in.
That wonderful image is courtesy John Seavey over at Mightygodking.com.
I feel a little bad to admit I spent most of the final scene of “The Angels Take Manhattan” being bothered by the blocking and apparent breaking of the weeping angels’ rules. Even if Amy closed her eyes, the Doctor and River both ought to have had the angel in sight.
So an alternate scene blossomed in my mind: Amy has her eyes shut, saying she wants to take the chance of the angel sending her back to Rory. She tells River to be a good girl. River closes her eyes, knowing this is what her mother wants. The Doctor, on the other hand, is a petulant child at first, not willing let go of his friend and let her choose her fate.
Amy bids the Raggedy Man goodbye with finality, telling him to let go. She’s chosen her life with Rory. With great reluctance, but admitting that Pond’s chosen her own way, the Doctor closes his eyes and the angel takes Amy.
That scene makes more sense to me, at least.
 Also, I find something tragic in that the Doctor could see Amy and Rory again, but for his own impatient nature. All he has to do is travel to a point in time before the angels infest New York City and wait for his friends to arrive, or travel to somewhere else on Earth at that point in time and get on a boat or a train. But the Doctor hates living second to second, so he’ll never do that.