The Giver, by Lois Lowry, is set in a futuristic dystopian / utopian society. Based on the evidence in the text, the place where Jonas lives seems to be a fairly small community. The community is by a river, which comes up often in the plot (at one point, a four year old boy name Caleb drowns in the river).
The various places within the community include:
The Nursery, the Nurturing Center, the Childcare Center, the Department of Justice, the school, the fish hatchery, the House of the Old, the Rehabilitation Center, the Hall of Open Records, the Hall of Closed Records, the Auditorium (where public events are held, such as the ceremony of twelves), and various family houses (called units or dwellings).
Also, there is a Annex, where the Giver / Receiver lives. It is special and noteworthy because it is the only place in the entire community that has locks on the doors, indicating the Giver / Receiver's unique status in the community.
A VERY important setting is also "Elsewhere," which is what the members of this community call anywhere that is beyond the community. At the very end of the novel, Jonas escapes the community and supposedly makes it to the mysterious "Elsewhere."