As far as time period is concerned, all of Twilight goes down in modern-time (technically around 2005, since that's when Meyer originally published it). The location of the action jumps around a bit, though. Read on for our Tour de Twilight!
Most of the story takes place in Forks, Washington, and its surrounding areas. According to Bella, Forks claims the highest rainfall per year in the United States. To put it bluntly, it's dreary and gray 99% of the time. The cloudy, rainy climate is one of the reasons the Cullens have chosen to live in Forks – because it's rarely sunny, they can go out in the daylight without having the sun sparkling off their glittery skin and exposing them. The dreary weather allows vampires to live relatively normal lives.
Another factor that distinguishes Forks is that it's surrounded by forests and wildlife. The woods are especially important to the novel, since the Cullens rely on wildlife for their diet. Not to mention, the damp greenery adds a "dark" element to Forks's location. You could say that Forks is the land of the dark.
If Forks is the land of the dark, Phoenix is the land of the light. When Bella hops on her plane to depart from Phoenix, it's 75 degrees and sunny. Bella, therefore, is a child of the light; she readily admits she prefers dry, warm climates.
When Bella first moves to Forks, she hates it. She tells us, "It was from this town and its gloomy, omnipresent shade that my mother escaped with me when I was only a few months old"(1.2). Later, Bella describes her feelings of confinement in Forks: "Thick fog was all I could see out my window in the morning, and I could feel the claustrophobia creeping up on me. You could never see the sky here; it was like a cage" (1.65.1-2). Over time, however, as Bella's relationship with Edward becomes more intense, Bella comes to like Forks. In fact, when she returns to Phoenix and is about to confront James, she says,
The sun was hot on my skin, too bright as it bounced off the white concrete and blinded me. I felt dangerously exposed. More fiercely than I would have dreamed I was capable of, I wished for the green, protective forests of Forks…of home. (22.81.4-6)
By the end of the novel, Bella has experienced a complete reversal in her feelings about the two locations.
The forest is an interesting setting for a number of scenes. Commonly in literature, the forest represents a wilderness where evil and/or mystery may reside. If you've read Nathaniel Hawthorne's The Scarlet Letter or Arthur Miller's The Crucible, you'll know what we're talking about. This may be the case in Twilight to some extent.
But in this novel (and in much of literature, including Shakespeare's As You Like It and A Midsummer Night's Dream, among others), the forest also represents safety from the confinement of society. The Cullens' home is nestled in the woods, away from the human world, and as Bella tries to sort out whether or not Edward is a vampire, she runs to the forest:
Here in the trees it was much easier to believe the absurdities that embarrassed me indoors. Nothing had changed in this forest for thousands of years, and all the myths and legends of a hundred different lands seemed much more likely in this green haze than they had in my clear-cut bedroom. (7.48.1-2)
A secluded meadow in the middle of the forest hosts Bella's first sight of Edward's skin when exposed to the sun. Bella describes the meadow almost like we'd imagine the Garden of Eden:
The meadow was small, perfectly round, and filled with wildflowers – violet, yellow and soft white. Somewhere nearby, I could hear the bubbling music of a stream. The sun was directly overhead, filling the circle with a haze of buttery sunshine. (12.257.2-3)
In this private setting, Edward can be himself in front of Bella for the first time. He shows her his super-speed and strength in addition to his sparkling skin. The meadow is also where Edward and Bella take their love affair to the next emotional level.
Lastly, La Push serves as the place of Bella's epiphany over Edward's "kind." Jacob Black, the son of one of Charlie's friends, fills in Bella on the local lore and informs Bella that the Cullens aren't allowed on La Push reservation. This new setting clues us into the competition between Jacob and Edward – each guy has his own territory on which neither can trespass, yet Bella is free to move between them.