1920s-1940s America, New York City
Ah, the city that never sleeps. The site of American ambition. The hustle and bustle of the Big Apple. There's really no other place that The Fountainhead could have taken place: New York City, like Roark, is mercilessly ambitious, restless, and individual. It's also (like Roark) rude, abrasive, and doesn't suffer fools gladly.
New York City is also full of buildings, many of which sort of act like characters in their own right. New York City is filled with Cameron's daring, and aging, designs, Keating's neo-classical copies, Roark's innovative and modernistic styles, Wynand's childhood slum and his grown-up penthouse. The face of New York is shaped and changed by the characters in this novel.
But the city isn't just a blank slate. It casts a sort of spell over many of the characters, like Dominique:
She stretched her arms wide. The city expanded, to her elbows, to her wrists, beyond her fingertips. Then the skyscrapers rose over her head, and she was back. (2.10.16)
While most of the book takes place in the city, we also get a few instances of people traveling to other, less populated, parts of America. These settings are mainly used as backdrops for Roark's designs. When natural beauty is observed, it is observed as potential material for building houses:
He looked at the granite. To be cut, he thought, and made into walls. He looked at a tree. To be split and made into rafters. (1.1.8)
Roark doesn't just pillage the natural world in order to get building materials, however. He also builds in harmony with the natural world, and the occasional jaunts to nature in The Fountainhead emphasize certain aspects of Roark's character.
But when these jaunts are over, it's back to New York, New York so that Roark can wake up to find that he's king of the hill, top of the heap.