Among the Hidden
Where It All Goes Down
The Garner's house and the Talbot's house
We may not know the exact where and when of Among the Hidden since Haddix intentionally left that bit of information out, but setting is much more than the latitude, longitude, and time table of a story. And Luke encounters two major settings: his narrow world on the farm, and the big scary world outside of it.
Beyond the Farm
On the farm, Luke's world is his family. As far as we know, he's never met another person outside his relatives; he never watches TV; he never passes the boundary of their woods. But he's just a kid, and with some brothers to tease him and a mom to pay him lots of attention, he's happy—until the woods come down, and Luke's narrow world gets a whole lot smaller.
Once the building begins, Luke spends most of his time in his "room" a.k.a. attic—just like another kid who had to hide from some major bad guys, come to think of it.
But then Luke rounds up the courage to sneak out of his house and all of a sudden his world becomes a little bigger. He meets another shadow child, a baron, and a revolutionary all in one shot. World: expanded. Once Luke meets another shadow child, he realizes that the world he was born into is a whole lot more complicated than he thought. The Government completely controls the people, telling them how many kids they can have, what land they can own, what they can do with that land, and basically every other tiny detail about their lives.
Country on lockdown
This totalitarian government is the plot's main antagonist and is what even gives us a story in the first place. But if you think about it, Luke's journey through the novel—from room to farm to the big bag world—is a lot like the journey every single person goes through while growing up. As you mature, your world gradually expands; you realize that you're not the only one like you in the world, and that your home life isn't the only way to live, and that there might actually be important work for you to do in the world.
Maybe Haddix doesn't give us a particular time and place because this is a story of all times and places: at heart, it's a story about growing up and becoming your own person, whether your family wants you to or not. And that's a story that could take place anywhere.