The story travels all over the world. Forest goes from his small town in Alabama to Vietnam and china. The movie starts in about the 60s or 50s. He visits the White House several times and the Capitol. The movie continues through at least the 80s.
The setting has a huge impact on the story, however due to Forrest's innoscenes the mood of the story rarely changes from the lighthearted feel even in the middle of a war scene. The setting changed the events that forest Gump went through such as the death of bubba never would've happened somewhere else and wouldn't have been a shrimp fisher. Although the places and locations are great and amazing, it's the characters that make the story.