When do you think the story takes place and why? What clues are given to help know this?

We don't know what period The Giver is set in..... only that it's set some fifty years in the future. Lowry noted in an interview; 

"No, it’s just some time in the indefinite future. It’s kind of interesting, I have a grandson who’s 13 and he asked me recently how far in the future it was. He speculated it was 50 years in the future, and the reason that came up is because the filmmakers had asked me how the boy’s bedroom should be decorated, and I said it should be very stark, nothing decorative on the walls, but maybe something educational like the periodic table of elements. And I mentioned that to my grandson and he said, ‘Fifty years in the future, there won’t be any helium anymore.’ Well, who knew, only a 13-year-old [laughs]. So you know, things of that sort would be very different, but who knows, the future seems to be speeding up and I read an article recently implying that very soon we will in fact be able to manipulate human memory. Whether that’s a good thing or a bad, we can only guess."