The Hunger Games, as a science-fiction dystopian story, takes place in the future. While the exact time period is never specifically revealed, what is apparent is that it seems to be post-apocolyptic, as those inhabiting the region of what used to be North America, have survived floods, droughts, fires, storms, hurricanes, and war.
The main character, Katniss, resides in this country, called Panem, which has been divided into 12 districts. Hers, District 12, is in the region of what was once the Appalachian mountains, and is a poor, coal mining district. Further, Katniss and her family live in the poor area of this very poor district. The poverty of District 12 is directly contrasted with the wealth of the Capitol, located near what used to be the Rocky Mountains. The central government of Panem is located in the Capitol, a shining city, filled with shallow but wealthy inhabitants.
The setting for The Hunger Games takes place sometime in the future (readers are never informed of the exact date or year), with what seems to be a time after some apocalypse. In North America, after various natural disasters that hit the earth and caused destruction to a greater part of the land, The Hunger Games provides for a setting that is greatly suited for the book and for the battle that commences as follows.
I forgot to further mention that the setting also takes place under a corrupt government, as is evident by its unethical intentions through the duel. This causes an oppressed society, with many to fall victim to the immoral practices of the government.