Our story takes place in a suburb of London called Richmond (which, yes, is part of London now). We don't see very much of the house in which it's set, just that it has a dining room, smoking room, laboratory, garden, man-servant, housekeeper, and maybe a cook. (We imagine it's a lot like Wallace & Gromit's house.) In this house in Richmond, surrounded by professional friends and nearly invisible servants, the Time Traveller seems somewhat insulated from the economic and political problems of the time. As the Epilogue tells us, however, he is aware of them, and he's not optimistic about the prospects.
Why not? What would it be like to live near London in the 1890s? Well, it would all depend on who you were. If you're the Time Traveller, you might wake up one morning to read an article in the newspaper entitled "White Slavery in London," describing a match factory whose women laborers suffer long hours, bad pay, and dangerous health complications from working with chemicals. (And it goes without saying that their employer offered them no health care.)
See, in Britain, as in the US, the 19th century was full of exciting new technologies – check out these Great Inventions of the Gilded Age for some examples. Technology was helping make industry boom, so everyone was happy, right? Well, not the factory workers, who made little money and worked insane hours at dangerous jobs. So the 19th century was not just a boom time for industry, but also for unions. (This page is about labor history in the U.S. at this time, as is this one, but things weren't all that different in Britain. Except they spell "labor" as "labour.")
And when we say "boom," we mean "boom" – like violent riots. Although not all strikes or strikers were violent, many people had the idea that the working classes were violent and revolutionary. Some strikes ended successfully. After the "White Slavery" article, for example, the match-girls' strike of 1888 worked out pretty well.
There was also some middle- and upper-class support for reforming the system so that workers would have better lives (not to mention die less frequently on the job). This was largely the work of various progressives. One notable progressive group in Britain was the Fabian Society, reformers who believed in gradual change. H.G. Wells belonged to that society for a while.
One more thing about the 1890s setting that serves as the frame here: while the Time Traveller doesn't necessarily seem like he ventures into the city very often, the other characters do. For instance, the narrator meets the Medical Man at the Linnaean Society (2.1), which was where Darwin discussed evolution in 1858.
In the year 802,701 we're still technically in the London area, but London no longer exists. The Time Traveller occasionally gives us his thoughts on that change; for instance, he notes that the Thames River, which is notoriously sedentary, has moved over a mile (4.15).
The Time Traveller spends a lot of time wandering around the countryside of the future ("the waste garden" [4.22]), but the two locations that seem most important are the Eloi's communal big house and the Morlocks' communal underground lair. The fact that everyone in the future lives communally sets them apart from the Time Traveller, who is kind of a loner in his small house in the 1890s. (Even though he has servants, we don't see much of them.)
Other than their communal aspect, the Eloi's ruins and the Morlocks' factory are very different, which contributes toward our understanding of them as mirror images of each other. The Eloi live a carefree, work-free existence in a dilapidated house filled with fruit. The Morlocks live in a functioning factory-like space, with a meat-heavy buffet (Eloi – the other white meat). So the setting in the future does a great deal of the work of characterizing the lazy Eloi and the monstrous, worm-like Morlocks.
The other significant location is the Palace of Green Porcelain, which turns out to be a museum. While the Eloi and the Morlocks show us one aspect of the fate of humanity (we're going to evolve into totally weird and different species), the museum shows us another. We may leave something behind, like a bit of writing that no one can read or a box of matches that still works, but we're mostly just going to disintegrate, like the library.
The Time Traveller ends his vacation where we usually start ours, on the beach. Except his beach is, first, full of butterfly and crab monsters, then empty, except for a black rock-like creature with tentacles.
These last images of the world – as the sun is dying and the earth slows down and eventually stops spinning completely – seem to place the rest of the adventure in a different light. Whatever happens to the earth and humanity over the next several hundred thousand years doesn't really matter, since eventually there's not going to be anything left anyway.