Okay, so we admit that setting might be a little confusing. Let's start with the easy one:
When this book was first published, in 1950, the first story took place almost 50 years into the future. When the stories were updated for the 1997 version, the first story took place almost 33 years in the future. (Presumably, the next edition will take place 20 or so years in the future.)
Most likely, Bradbury set the novel in a time far enough away so that new technology would be plausible (yay interplanetary rockets) but close enough that we still wouldn't have figured out some of those pressing global-civilization issues (boo nuclear weapons).
"Rocket Summer," "The Taxpayer," part of "The Fire Balloons," "The Wilderness," "Way in the Middle of the Air," and "There Will Come Soft Rains" all take place on Earth. That's six out of 28 stories, so we're definitely going to be spending most of our time on Mars.
And when we do see Earth, it's looking like a pretty ordinary, 1940s-style Earth, even if it is supposed to be 1999 or 2034. We have "children skiing on slopes, housewives lumbering like great black bears in their furs along the icy streets" ("Rocket Summer," 1), and the narrator even tells us in "The Taxpayer" that it's an "ordinary Monday morning on the ordinary planet Earth" ("The Taxpayer").
Something kind of interesting: evidently Bradbury's future included rocket ships, food pills ("The Wilderness"), and nuclear war, but not any kind of gender equality. Even when the house is fully automated (as in "There Will Come Soft Rains"), the dad still comes home at night and gets his cigar lit while the mom does her errands.
Time for a brief history lesson!
In 1877 an Italian astronomer named Giovanni Schiaparelli noticed that Mars had these funny lines that looked like natural formations. He called them "canali," or "grooves," which got mistranslated as "canals." Suddenly, everyone on Earth thought Mars was inhabited by intelligent Martians who built canals to bring water to their cities. They thought of Mars as a dry place where a great civilization was probably dying out. American astronomer Percival Lowell even wrote two books about the peaceful Martians and their canals: Mars and its Canals (1906) and Mars as the Abode of Life (1909).
This brings us to early science fiction, like Edgar Rice Burroughs's books on Mars (now a major feature film). As Burroughs imagined it, Mars was dry, dying out, and full of telepaths. Sound familiar? Bradbury doesn't deny it. In fact, he's said that Burroughs's books really inspired him as a kid.
In other words, Bradbury's version of Mars is not so much the way people thought of it in the 1940s and 1950s, when he was writing. His Mars is more like the one people were writing about in the 1900s and 1910s—set in the future, but inspired by the past.
Even before humans get to Mars, Mars seems a bit like an American suburb. Take "Ylla," with its depressing portrayal of how "marriage [makes] people old and familiar" ("Ylla"), or "The Summer Night," where people go hear music and kids sing nursery rhymes. Sure, some details are different—Ylla uses magnetic dust instead of, say, a Swiffer ("Ylla," 1)—but most of it looks a lot like Earth.
Probably more than anything else, Mars in this book is like America when Europeans first came to settle it, and later when Americans pushed the frontier westward. This comparison comes out in certain parallels:
1) Hey, there are already people living here! Oh, oops, we gave them all chickenpox and they died. Plus, we shot some of them and destroyed their culture.
2) People settle in hard-living mining towns.
3) The chef of the Fourth Expedition is named Cookie, which, uh, was apparently a loving nickname for chuckwagon chefs ("—And The Moon Be Still as Bright," 134).
In case we can't pick up on these clues, Bradbury lays it out for us directly a few times:
The picture that we're getting here is that this may be a fantastic version of Mars, but it's not about space travel and exploration so much as it's about the frontier of America.