In which year does The Giver take place?
An unknown year in the future.
Lois Lowry, the author, was asked this question in an interview with Buzzfeed:
Do you ever say what time period The Giver takes place in?
LL: 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.
So we know for sure she wasn't aiming for any very specific time period, which means there are almost certainly no clues in the novel fixing it to a particular year. The thing about "50 years in the future" is hardly canonical in any sense of the word, but it's just an interesting factoid, and the author mentioning it suggests that near future (21st century) is at least plausible.