Lord of the Flies takes place on an uninhabited island in the Pacific Ocean. It is tropical, with palm trees and a coral reef.
Golding tells us that the island is "boat-shaped", with a jungle at one end and a rocky mountain above it. At the opposite end is the lagoon where the boys first meet after their plane crash. The island is a very isolated place, and has no contact with the outside world.
We can only assume that the year is roughly around the time Golding was writing (early 1950s), when the United States was engaged in a deadly struggle with the USSR for nuclear supremacy.