There is no specific location or date given for the action in the story of The Giver. This is not coincidence; the themes and lessons of the story are meant to be potentially applicable in any location and period in time.
The story obviously takes place at some time in the future. The advances in use of medications to control physical conditions and mental processes indicate that medical science has advanced from where it exists in today's reality. The common use of euthanasia and the political structure of the community also reflect a society that has evolved significantly from today's social and cultural attitudes.
Location is harder to detect. With the adoption of Sameness, weather changes due to seasonal variations have apparently been eliminated. The community's members do not have experience in dealing with snow or cold weather but no mention is made of extremely hot weather, either. It may be that the community is located within some sort of facility that artificially controls climate.