Most of the races in Eberron are found in most of the countries; it’s a fairly cosmopolitan world. The ir’Wynarn royal family that ruled the Kingdom of Galifar before the Last War was human, but Galifaran society was a mix of human, elf, half-elf, gnome, and halfling, with a large smattering of other races in greater or lesser amounts. Though the Kingdom of Galifar is over, the culture of most of Khorvaire is still Galifaran.
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Humanos originated on the continent of Sarlona, far to the east, but have been in Khorvaire for thousands of years. By the time, nearly a thousand years ago, that the human king, Galifar ir’Wynarn, conquered and unified the “human” Five Nations, those nations comprised most of Khorvaire’s center, and also boasted large, integrated populations of elves, half-elves, halflings, and gnomes. The ir’Wynarn royal family would rule over the Kingdom of Galifar, which would expand to include all of Eberron as well as one port city in Xen’drik, Stormreach, until the Last War. In the end, five children of Galifar’s last king disagreed about who ought to ascend to its throne, and the Last War broke out.
The four remaining Five Nations, Aundair, Breland, Karrnath, and Thrane, are human-majority countries, and each is still ruled by a human. Aundair, Breland, and Karrnath have monarchs from the ir’Wynarn family (though King Kaius III of Karrnath is secretly a vampire—and also secretly King Kaius I, who started the Last War to begin with). Thrane is a theocracy ruled by the Church of Silver Flame, which is led by the Keeper of the Flame, who is chosen via prophetic visions. The Keeper of the Flame need not be human, but most of the Church’s faithful are human, and in any event, all Keepers at least since the Church took over the country have been human.
In addition, there is still a vast human population in Sarlona—quite possibly larger than Khorvaire’s. They are, by an enormous margin, the most common race in Sarlona, both in the vast empire of Riedra and in the small, mountainous country of Adar. However, humans do not rule either country—Riedra is ruled by the quori, nightmare beasts from the moon Dal Quor, and Adar is “ruled,” such as it is, by the kalashtar, humans bonded with the quori’s benevolent cousins. Both quori and kalashtar are heavily outnumbered by regular humans, though. The quori use heavy propaganda and an oppressive police state to keep their human population in line; the kalashtar have, perhaps unsurprisingly, a more symbiotic relationship with their human brethren.
So all told, a human could come from anywhere in Khorvaire, or from Sarlona, or even from Xen’drik (the city of Stormreach).
Elfos originated in Xen’drik, the continent to the south of Khorvaire, but only the drow are still from there. Non-drow elves all moved to Aerenal, a large island between Xen’drik and Khorvaire. A big chunk of the elven population left Aerenal a couple thousand years ago, when House Vol was destroyed and House Phiarlan decided Aerenal wasn’t safe for them either; as such, elves can be from anywhere in Khorvaire. Another chunk of the Aereni elf population has recently founded the nation of Valenar, in Khorvaire, but most of Valenar’s infrastructure remains in Aerenal, and all “Valenar” elves are born and raised on Aerenal and only come to Valenar as young adults. See this answer for more details on Eberron’s elf populations.
Meio-elfos in Eberron are more often the children of two half-elven parents than they are the children of an elf parent and a human parent—the latter isn’t too uncommon, but the existing population of half-elves is just a great deal larger. The half-elves don’t really have any nation of their own, since they originate with the humans and elves of Galifar, and that nation spanned the entire continent. House Lyrandar’s headquarters on the island-city of Stormhome is a majority-half-elven enclave, though, and some half-elves consider it “theirs.”
Halflings are one of Khorvaire’s native peoples, originating on the Talenta Plains. They were also the first race to exhibit a dragonmark, Gallanda’s Mark of Hospitality. Traditional nomadic halfling culture still exists in the Plains, and House Gallanda in particular is a big steward of that culture, maintaining the one permanent settlement in the country, Gatherhold, for the halflings. Many halflings, including notably House Jorasco, have long-since left Talenta however, and are now found throughout Khorvaire.
Gnomos, another native, are from Zilargo, but again, a really cosmopolitan race found throughout Galifaran society. More so than elves and halflings, though, gnomes tend to like their nation’s society (which is a bureaucratic nightmare to everyone else), so a gnome is somewhat more likely to actually be from Zilargo than another nation.
Anões are from the Mror Holds, specifically from one of twelve clans. They have been integrated into Galifaran society for over a thousand years (before Galifar himself, even), so a dwarf from any of the remaining Five Nations would be unsurprising, and a dwarf from anywhere else in Khorvaire wouldn’t be too weird either. Still, being more secretive and communal than many of Khorvaire’s other races, dwarves tend to continue to think of the Holds as home. Dwarves are rumored to have originally hailed from a now-frozen continent to the north, but even if so, that continent is uninhabitable now.
Orcs are another people native to Eberron, and are primarily from northwestern Khorvaire—the Eldeen Reach, the Shadow Marshes, the Demon Wastes. They have a druidic culture that regards itself as the protectors of the world—and indeed, they have a long history of fighting against fiends and the madness beasts of Xoriat. The Demon Wastes, in particular, has little-to-no actual inhabitation, but rather a series of orcish war-camps that fight against the slow leak of fiends from the caves to Khyber found in the Wastes’ myriad cracks and canyons.
Half-orcs basically show up anywhere humans and orcs intermingle, primarily the Eldeen Reach and the Shadow Marches, though half-orcs joining up in the fight against fiends in the Demon Wastes isn’t too unusual. House Tharashk, with the Mark of Finding, is a mix of humans, orcs, and half-orcs based out of the Shadow Marches.
Goblinoids (bugbears, goblins, hobgoblins, etc.), also native, had an empire, Dhakaan, ten thousand years ago that even more thoroughly dominated Khorvaire than Galifar did, and can be found just about everywhere. More recently, the nation of Darguun was founded by and for goblinoids as an attempt to recreate the power and prestige of Dhakaan. Goblins aren’t especially likely to be de Darguun, but Darguun hopes, at least, that they would consider moving para lá.
Shifters, who are long-removed descendants of lycanthropes, are found primarily deep in the forests of the Eldeen Reaches. They tend to a druidic hunter–gatherer lifestyle.
Lagarto are the natives of Q’barra’s jungles, though they can also be found in the Shadow Marches. A lot of them worship the Dark Six, the Dragon Below, and/or fiends in general, though not all.
Dragonborn were basically a dragon experiment shortly after the destruction of Xen’drik, before they more thoroughly removed themselves from the world. They are found pretty much only in Q’barra, where they have a mini-empire that was nominally founded to fight against the fiends and fiend-worshiping lizardfolk in the jungle there. They forgot about that, then got messed up by fiends, and remembered it, and now do a little bit more to try to keep the fiends in check. Most of Khorvaire couldn’t tell a dragonborn from a lizardfolk and wouldn’t care if you told them. (Basically, in 3.5e, dragonborn weren’t even a race, so Eberron materials didn’t need to handle them, and when 4e and then 5e made dragonborn a core race, the way to handle them was to stick them in the jungle alongside the lizardfolk and say they were always there, the humans just didn’t realize they were different.)
kobolds are found basically wherever there are mountains. They can even be found in Xen’drik, since they travel underground through Khyber to other parts of the world.
Minotaurs are known to be found in Droaam, though probably not exclusively.
Centauros can be primarily found in the Eldeen Reaches, probably most often in the less-densely-forested areas in the eastern side of the country.
Changelings are a tiny fraction of the population, and tend to live in urban—which for Khorvaire, means human-majority—areas. There isn’t really any such thing as a changeling society, and changelings are about as unlikely to recognize each other as everyone else is. Some changelings live their almost entirely in one form, just living as that person, others change form as it suits them, and others live their lives primarily in their default form, rather than taking on others.
Kalashtar are from Sarlona, far to the east, and have only relatively recently come to Khorvaire. Most still are from Sarlona, but a number have fled Riedra and the quori, and can be found primarily in Sharn, which is where the ships to and from Sarlona primarily land in Khorvaire.
Forjado em Guerra were artificially created in the Creation Forges of House Cannith. Most of those were in Cyre, and destroyed in the Mourning, and the remainder were shut down as part of the Treaty of Thronehold. Merrix d’Cannith secretly operates a Creation Forge out of a laboratory hidden deep within the city of Sharn, in Breland, and the self-styled Lord of Blades operates a malfunctioning Creation Forge in the Mournlands, but that’s it. Each of the Five Nations bought warforged in large numbers, so they can be “from” any of those nations, though many don’t really consider themselves to be “part” of those nations. (Officially, per the Treaty of Thronehold, they estão citizens, though.) The closest thing to a warforged nation is the Lord of Blade’s army in the Mournlands, but that doesn’t appeal to the vast majority of warforged. Originally, and this is a secret known to very, very few within Cannith’s upper echelons, the Creation Forges came from Xen’drik, and many millennia ago (before the elves reached Aerenal, even), the quori created warforged there—though they lacked the true sentience of Cannith warforged.
Tieflings, of course, can be found nearly anywhere, but the Shadow Marches are the most common place for them, since there are relatively more caves to Khyber there. (Also, the people there often worship darker powers and so might have more contact with fiends, or be more comfortable with existing tieflings and willing to perpetuate that line.) The Demon Wastes also have tieflings, but most of those are going to be thoroughly in thrall to the demons and probably not an ideal player character in most games.
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Aasimar are very rare in Eberron, and more likely to be found as a result of a blessing or “chosen one” than from an actual relationship between a celestial being and a mortal. This is the only suggestion that Guia do Wayfinder para Eberron offers, for example.
That said, several of Eberron’s moons have celestial inhabitants: archons in Irian or Shavarath, guardinals in Lamannia, angels in Syrania. (Eladrins were celestial in 3.5e, but aren’t any more because of dumb fiddling; they were always from Thelanis in Eberron though.) Each of the moons (except Dal Quor and Xoriat, which are not relevant here) have “coterminous phases” where travel between the moon and Eberron is far easier (in fact, it’s possible to do it accidentally), and they also have “manifest zones” which are areas of Eberron that are always linked with a particular moon, even when it is not coterminous. These times and places give opportunities for celestials to possibly meet and form relationships with mortals to produce aasimar “the old-fashioned way.” This may mean—arguably—that more aasimar are born in Sharn (Breland) than anywhere else, just because Sharn is the most populous city on the continent, and it’s also built on top of a manifest zone to Syrania, where angels reside.
Yuan-ti are found in Xen’drik. Civilization is broadly not possible Xen’drik due to its sundering and curse, so at best they can form relatively small city-states there. They are not well-known, at all, in Khorvaire.
Various “monstrous” races are found throughout Khorvaire, but there is the fledgling nation of Droaam, which is trying to become a recognized “home” for such creatures. No one else recognizes Droaam as a thing, though.
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Other races are only mentioned extremely briefly in Guia do Wayfinder para Eberron; Tritons and Tabaxi are literally their examples of races that they don’t cover, and previous editions didn’t either. Eberron has a general maxim of “everything in D&D has a place in Eberron,” but where exactly these would go is unclear.
Firbolgs are giant-kin, which probably means they’re from Xen’drik and not doing very well. Alternatively, they are rather druidic, which means maybe in Eberron they aren’t related to giants, but instead to druids or maybe even shifters, or otherwise their own race out in the deep forest of the Eldeen Reaches.
Tabaxi are jungle-dwelling, and so your options are basically Q’barra or Xen’drik. Guia do Wayfinder para Eberron offer Xen’drik as an example of where you might decide to put them in your game, for what it’s worth, and that kind of makes sense since the denizens of Q’barra tend towards the scaly rather than furry.
Kenku are also mentioned in Guia do Wayfinder para Eberron as an example of how to handle unhandled races, suggesting that maybe in your game, there could be a nest of Kenku atop Sharn’s tallest tower. That... seems kind of dumb to me, to be honest, just because that’s not really enough for a population, doesn’t explain where they come from or where they fit in, and also doesn’t explain why the rest of Sharn isn’t aware of them, since “the tallest tower in Sharn” isn’t exactly a remote and inaccessible location like a Xen’drik or Q’barra jungle is.
Tritões are not explicitly described in Eberron material, but the sahuagin are known to primarily live in the Thunder Sea between Khorvaire and Xen’drik; this seems a relatively likely place for tritons as well.
Golias are easily claimed to just be hiding up in the mountains somewhere, possibly between Q’barra and the Blade Desert, which is a particularly desolate stretch. Alternatively, Guia do Wayfinder para Eberron does give them as an example of how a DM can “change the world” by making Darguun a goliath nation instead of a goblin one (I, for one, think this is a dumb idea).
Loxodons, as elephant people... I have no idea, they could really go anywhere. Probably the Eldeen, they seem like they’d get on well with the general druidic vibe there.
Vedalken may well be from Daanvi, the Moon of Perfect Order, though again, anywhere out of the way kind of works. Using Vedalken stats for the Inspired of Riedra might work, too.
Simic Hybrid are probably Daelkyr abominations. I would probably use the fluff for Daelkyr half-bloods from Magia de Eberron for Simic hybrid characters, since we have no 5e stats for Daelkyr half-bloods. The Daelkyr are the madness lords of Xoriat, and many of them are imprisoned within Khyber after Xoriat’s invasion of Eberron some 10,000 years ago. The corrupting influence of the fleshwarpers is still sometimes felt in Eberron, and they are by-far the most likely source of something similar to a Simic hybrid, as neither the Simic Combine nor anything particularly like it exists in Khorvaire society. (There is also Mordain the Fleshweaver in Droaam, but he is easily competitive for the title of “dumbest thing included in Eberron” and should just be ignored.)