I know this is a fools errand, but it's also a fun bit of extreme nerdity, and the release of CEE has reignited this little thread of interest. however, I do think that you can analyze both the in-game material and the larger Conan corpus and make an informed guess as to where the Exiled Lands are (and I do believe they are a physical location in Hyboria). Some spoilers for in-game lore, if you are a new player, continue at your own risk (if you are old player, continue at your own risk, as I went deep on this).

Legend:

CL = Conan Lore, materials from the stories and scholarship. The game draws heavily from all Conan canon.

CE = Conan Exiles, materials unique to the game

Sources noted in brackets.

Chronology

CL: The Serpent Men were the rulers of Valusia, a Pre-Cataclysm nation located on the western coast of Thuria, driven south by the Atlantian Kull. Surviving Serpent Men were found in the Black Kingdoms south of Stygia by Conan’s time (Shadows in the Skull).

CL: On the eastern coast of Thuria were the Khari. The Khari survived the Great Cataclysm, and enslaved the Lemurians refugees who arrived from their now destroyed island. The Giant-Kings meanwhile ruled over Thurian-era Stygia in a city named Luxor. After the Cataclysm, Luxor was suddenly located in the middle of hostile desert, so they packed up and moved to a large, fertile, northward-flowing river valley to their west, which they called the Nilus, which emptied into a small salty inland sea. The citadels of Kuthchemes and Pteion were built during this period (The First Great Migration).

CL: 500 years after the Great Cataclysm, a lesser cataclysm caused the Nilus sea to drain westward to the ocean, becoming western leg of the Nilus River; this same cataclysm created the Sea of Vilayet far to the northeast. The Giant-Kings also expanded westward along this new river, eventually stretched all the way to the Western Ocean, and building a new capital city named Luxor along its shores (The First Great Migration). At the mouth of the river Nilus they built Khemi, which became their commercial port. They explored to the north and established colonies along a northern river they called Acheron, discovering ruins of ancient Pre-Cataclysm Valusian cities, and magic relicts within. For 1000 years, the Giant-Kings subjugated the nomadic tribes along the Nilus river (Acheron Revisited).

CE: The Exiled Lands had rolling grasslands and temperate hills; this condition was dependent on the existence of the dam (The Great Dam lorestone). It was bordered by desert in the south and west, where “savages make endless war upon each other” (The Broken Highway lorestone), mountains in the north, and a swamp in the east (Lemurian lorestone #6). The mountains became snowcapped after the arrival of Frost Giants (Temple of Frost lorestone). The sandstorm desertified the previously fertile lands (Petruso).

CE: The Unnamed City is the capital of “the empire,” where the Triumvirate rules (The Dawn Gate lorestone).

CE: The Lemurians escaped the Cataclysm, moved west and taken by the Khari, a group escaped and moved west, arrived at the Vilayet, escaped those waters and continued to move west, then arrived in the lands of the Triumvirate (Lemurian lorestone #3-5). The river existed before the Lemurians arrived, and is how they navigated to the Unnamed City (Sentinels lorestone).

CE: The Lemurians discovered surviving Serpent-Men beneath the mountains, demanded that the Triumvirate break off their alliance with the Serpent-Men, which was denied and led to the war (Lemurian lorestone #10).

CL: 1500 years after the Great Cataclysm, the Khari were destroyed when the Lemurian slaves successfully rose in revolt. The Khari survivors fled west, eventually reaching the area south of the Sea of Vilayet at the edge of the Kharamun desert, and learned of the lands of the Giant-Kings. As they moved west, the Khari first encountered the eastern citadel of Kuthchemes. The under-defended city fell quickly. The Khari used Kuthchemes as a base to attack and capture the Giant-King cities along the Nilus. Giant-King refugees fled by ship to their northern colonies along the Acheron. The Khari took control of the Nilus River, renamed it the river Styx, and called themselves Stygians (The First Great Migration).

CE: Some time after the Triumvirate were defeated by the Lemurians, the Khari came to the Exiled Lands, settled a city west of the Unnamed City, which was later lost in an earthquake (Age-worn Scroll).

CL: Thugra Khotan, a dark sorcerer, reigned in Kuthchemes three thousand years ago, “when the kingdoms of Stygia stretched far northward of the great river, over the meadows of Shem, and into the uplands.” Thugra Khotan was “the last magician of Kuthchemes,” when “gray-eyed, tawny-haired barbarians in wolfskins and scale-mail had ridden from the north into the rich uplands to carve out the kingdom of Koth with their iron swords. They had stormed over Kuthchemes like a tidal wave, washing the marble towers in blood, and the northern Stygian kingdom had gone down in fire and ruin.” (Black Colossus)

CL: Kuthchemes was located in the mysterious desert expanse lying southeast of Shem. “A few days’ ride on camel-back to the southwest” would put a traveler within “sight of the great river Styx at the point where it turned at right angles with its former course, and flowed westward to empty at last into the distant sea.” To the east, “the desert shaded into steppes stretching to the Hyrkanian kingdom of Turan, rising in barbaric splendor on the shores of the great inland sea. A week’s ride northward the desert ran into a tangle of barren hills, beyond which lay the fertile uplands of Koth, the southernmost realm of the Hyborian races. Westward the desert merged into the meadowlands of Shem, which stretched away to the ocean.” (Black Colossus)

CL: 2500 years after the Great Cataclysm, the Stygian border has been driven to the banks of the Nilus, by the peoples of Shem and Koth, both of whom have been subjugated by the Stygians for the past 1000 years. 500 years after that, or 3000 years after the Great Cataclysm, is the beginning of the "Age Undreamed Of,” during which time is the Age of Conan (The Hyborian Age).

CL: The isle of the wizard Siptah is located off the coast and south of Khemi, at the mouth of the Styx (The Gem in the Tower).

CE: The Exiled Lands can be traveled to (at least partially) via ships coming from Argos (Isle of Siptah introduction), and from the south on foot/by cart (The Broken Highway lorestone). Foot and caravan travel is within marching distance of Stygia (Age of War battlepass).

CE: Thoth-Amon was able to journey to and from the Exiled Lands during his early days (Mek-kamoses), and Stygia was the first to send Exiles. Ctesphon was at first unaware that other lands were sending Exiles to the Exiled Lands.

CL: Thoth-Amon obtained the Serpent Ring of Set in a tomb deep beneath the earth, early in his career as a sorcerer. During the reign of King Conan, it was stolen from him, causing Thoth-Amon to flee from his rivals, and attempted to reacquire the ring. (The Phoenix on the Sword)

CL: Travelling from Koth in the direction of Kuthchemes is described thus: “On the southern side the hills fell away sheerly, marking a distinct geographical division between the Kothian uplands and the southern desert. The hills were the rim of the uplands, stretching in an almost unbroken wall... Beyond the hills the desert stretched bare, dusty, lifeless… Promontories ran out into the desert, forming barren valleys, all but one of which were closed on the northern extremity by rugged cliffs. The desert lay bare to the gaze, though just now this view was limited by low-lying clouds which rested in whitish masses on the southern horizon. The monotony was broken only by a jutting tangle of stone ruins, some miles out on the desert, reputedly the remnants of an ancient Stygian temple.” (Black Colossus)

CE: Pirates have been brought to the Exiled Lands, including ones with experience on the Vilayet (Jamilia) and on the ocean (Shamalla) and are drawn to the organization and iconography of pirates, but the eastern swamps have no definite connection to either location of piracy, only that they wish to return to open water (Jamilia; Shamalla).

CE: King Ctesphon sends legions into the Exiled Lands, and they must carry everything with them. “Provisions and other resupply must be found along the way.” (Age of War battlepass)

Observations

• The sun rises in the south and sets in the north in-game. This was done for mechanical reasons pertaining to the way shadows fell during development. If this were accurate to the map, it would mean that the jungle would be north, the volcano west, Sepermeru south, and the Broken Highway east. However, there is a large volume of in-game materials that clearly establish elements on the map existing in directions if the map is oriented with north being the top of the map. These two things are incongruous, and you must choose which is more important to you: the in-game experience or the material evidence. I choose to interpret the map as oriented with north as the top. [Edit: apparently with Enhanced, the sun's direction has been corrected, so there is no longer an incongruity and the in-game textual evidence aligns with the sun!)
• The Conan Exiles map is approx. 30.5 km^(2) (each square is about 500 x 500 meters, and there are 122 accessible squares on the map). I suspect that this map is meant to be representative of the lands, not exact in size. The CE default time dilation is a full day/night cycle in 30 minutes; 1 minute playing represents 48 minutes to the character. Lowie on YouTube walked across the map from Sepermeru to Xel-Ha and it took 1 hr 24 minutes of real time, or 67.32 in-game hours. If we assume an average walking speed of 5km/hr for 67.32 hours, that puts the width of the map at 337 km, or a scale of 61x the in-game size. Each square would be around 30 x 30 km, or 900 km^(2), and the whole accessible map balloons to 113,500 km^(2). That’s just slightly smaller than Pennsylvania, or just larger than Cuba.
• The rolling grasslands and temperate hills of the Exiled Lands described by the Lemurians is preserved in the Crowngrove.
• The river appears to be fed, at least partially, by the dam. This suggests that the river is partially Giant-King made, in order to make the desert habitable. It is also possible that the current river has been greatly enhanced by the increased runoff from the melting and replenishing snow and ice unnaturally clinging to the mountains.  
• The Dawn gate lorestone states “You have come as bidden, to the heart of our empire. Behold the glory of our capital, where the triumvirate rules.” It does not seem, based on the history of the Giant-Kings, that the Unnamed City is the capital of their entire empire, which is established to be the second Luxor during their high period. I think a better interpretation is that this is the Triumvirate’s capital, a city state within the larger Giant-King sphere of influence.
• The Khari appear to have had no interaction with the Lemurians. It is possible that, when the Khari invasion happened, since the Unnamed City was already abandoned, they did not significantly investigate the surrounding area, or their small settlement existed briefly before being destroyed.
• The math of when Thugra Khotan reigned in Kuthchemes makes more sense as being 3000 years since the Great Cataclysm, as that would put him in the time period of Koth pushing the Stygians south. Howard's dates in general have issues.
• Darfari like Nunu are not wearing a jeweled bracelet, implying that they inhabit this area indigenously or nomadically, not because they were Exiled.
• A vast amount of the animals we see in the game are animals endemic to Africa, including lions, elephants, rhinos, ostriches, gorilla, crocodiles, gazelles, panthers, and hyenas. The next most common would be traditionally European animals like Sabretooths, Mammoths, smaller lions, and bears.
• An Exile was placed on a ship in Argos and sent south, before getting wrecked on Siptah, near Khemi. However, all Exiles are implied to enter the Lands via the Broken Highway. I think this suggests an economy, or at least a convenience, for western Hyborian nations to ship their Exiles to a port on the eastern coast, and the Exiles are sent via caravan to the Lands. If the wrecked ship were heading for Khemi, it may be that Exiles are shipped up the Styx.

Possible Location

Given the textual evidence, I do not think that the Unnamed City is Kuthchemes. However, I do think, given the similarities between the description of the surrounding lands to Kuthchemes and the Lemurian’s initial description of the Giant-King's lands, I think a reasonable analysis is that the Unnamed City is in a similar location to Kuthchemes. Part of me is tempted to say that the Unnamed City might be the original Luxor (which would explain the "the heart of our empire" description, as this would have once been true), which was claimed by the desert during the Cataclysm, reclaimed by the Triumvirate for their own purposes, but that is pure supposition.

However, I think a reasonable argument can be made that the Exiled Lands exist someone in the unclaimed northwestern territory of the Eastern Desert, east of Shem and northeast of Stygia, and flanked by mountains in the north (either the mountains of Koth or Khoraja itself, or an isolated range in the desert). This location would put it within marching distance of Stygia and whatever caravan route takes the Exiles to their doom. This location would also put it in range of a young Thoth-Amon’s journeys, buoyed by ancient writings and whispered myths. It would not be a location though that many would stumble upon accidentally. The swamps, as described in-game, were likely created by the river in a lowland area, and then the increased water flow from the tundra melt over the millennia has allowed those ancient swamps to swell into an isolated freshwater lake, of which we see a sliver to the right of the map (possible that pre-Cataclysm this was a verdant area as Luxor-of-Old once was, and the river and lake fill long dry beds from the past).

Resources:

Dale Rippke’s “The First Great Migration”

Dale Rippke’s “Acheron Revisited”

Howard’s “The Hyborian Age”

Howard’s “Black Colossus”

Howard’s "The Phoenix on the Sword"

Sprague de Camp and Carter’s “The Gem in the Tower”

Sprague de Camp and Carter’s "Shadows in the Skull"

No sarcasm; when this set was announced, I thought "I really want that Wong and Bats, but have no need for a sweaty Dr. Strange." Was randomly looking on Kijiji the other day and someone who only wanted Dr. Sweats was getting rid of these guys, never been taken out of the packaging. Yay me!

Hope this ok to ask. Recently moved into a house with this set up in the backyard. Natural gas line runs into the garage for a heater in there, but has this spout off the side next to the deck, seemingly a natural place to put a bbq with a gas line. I've only ever had propane BBQs, so just want to know if this is in fact a set up for a BBQ, and if it is safe for me to remove the cap myself to install the hose for the Q. Any advice is appreciated.

Hope this is ok. My experience with backyard BBQs is entirely propane based. We bought a house with a natural gas outlet, and were gifted a BBQ with a natural gas option. Need to buy the kit to connect one to the other. I know that I need to know the inside diameter of the gas pipe. Right now it's plugged with a stopper (pictured) stamped 1/2. I assume that this means it's a 1/2 ID connector that I need, but just want to be sure (included the top of the connection incase that makes a difference). Any help would be appreciated.