If ein Arímoisin can be translated "among Arimoi" then it would appear that Hesiod is naming the tribe or nation—the Arimoi—among whom Ekhidna [Echidna] is keeping guard rather than necessarily her geographical location, although location might be implied therefrom. As for what she is guarding, I would try to connect her to the oracle at Delphi based on some passages from other mythographers.
Immediately after the Theogonic line in view, Hesiod supplies the genealogical information on the most popular monsters in Greek myth, roughly half of whom are the offspring of Ekhidna by her husband or mate Typhoeus, a cosmic fire-breathing storm-giant. Hesiod goes on to finish breaking down the divine family tree at this level and narrating the conflict between Zeus and his father the Titan Kronos before eventually getting back to Typhoeus, who is brought forth by Gaia to avenge Kronos. Typhoeus ultimately fails, however, and like his half-brother Titans he too is cast into the Underworld storm-pit of Tartaros, which storm-pit is actually the giant's own father.
Apollodorus' version of the contest between Zeus and Typhoeus is particularly striking for its remarkable feature of having Zeus, at some point, veer extremely close to actually being destroyed by Typhoeus. In his Bibliotheka Apollodorus says that Typhoeus dwelt in something called the Korykian [Corycian] Cave in Kilikia [Cilicia], Asia Minor. This mythographer's placement of this cave in so far away a corner of the Mediterranean Basin is surprising considering that the cave's name is typically associated with Mt Parnassos, and the city and oracle of Delphi in the Phokis region of Greece. In his book Drakon: Dragon Myth and Serpent Cult in the Greek and Roman Worlds, Daniel Ogden muses that it might have something to do with a Hittite Chaoskampf or combat myth being the origin of the contest between the chief Greek storm-god and this immense serpentine creature.
Apollodorus continues by saying that in the vicinity of Mt Kasios on the border of what is now Syria and Turkey, after a furious battle between Zeus and Typhoeus, the giant managed to incapacitate Zeus by coiling around him and even tearing out the sinews from the god's hands and feet, presumably paralysing Zeus at least for a time. He then deposited the wounded deity in this Kilikian lair of his: the Korykian Cave. Now either Typhoeus did not have the ability to kill Zeus or he was being a typical James Bond movie villain, buzzing off to go do something else while leaving his arch-nemesis in the custody of some henchman or other.
Whatever the giant's intention had been, he is described as having carried Zeus on his shoulders across the sea to Kilikia, where he deposited him in the cave.
Likewise he put away the sinews there also, hidden in a bearskin, and
he set to guard them the drakaina Delphyne, a maiden who was half
beast. But [Zeus' sons] Hermes and Aigipan stole the sinews and
while nobody was looking, reconnected their father with these body parts. Zeus was able shortly afterwards to vanquish Typhoeus for good.
Sir James George Frazer's translation of this passage says that Zeus was carried through the sea. Maybe I'm making much of a muchness out of that but then what if therefore the Korykian Cave (and ultimately the Arimoi?) should be located underwater? It would make sense of the form which Aigipan is said to have taken for this rescue mission, changing himself into the "Sea-Goat," a goat whose hind quarters were a fish-tail, which creature was afterwards placed in the sky, in his honour, as the constellation Capricorn.
This location for the Korykian Cave may create other problems, though, as other writers, such as Callimachus, derive the origin of the name Delphi from the drakaina Delphyne, who in this version of the myth replaces the more famous dragon Python. In the Homeric Hymn to Apollon [Apollo], Typhoeus is called Typhaon, he is the fatherless son of an enraged Hera, who deposits him, after his birth, with the evil drakaina dwelling at the site of Delphi, apparently none other than Delphyne.
When Apollon makes his début at the site, he slays the drakaina and thus founds the Pythian oracle through which the land's inhabitants can offer him sacrifices. Based on the connection between Delphyne and Typhoeus in the Bibliotheka, Aaron Atsma determines Delphyne to be the same personage as Ekhidna.
Robert Graves' interpretation of all this in his book The Greek Myths is a bit more complicated, as he insists that Typhaon is here to be equated with (a definitively male) Python, who then becomes the consort of Delphyne.
Typically the Korykian Cave appears on Mt Parnassos in order to connect Apollon's dragon-slaying effort with the establishment of his shrine in the major city which is founded there (usually built by his son Delphos or by Apollon's cousin likewise named Delphos).
An alternate solution might be to say that the Arimoi, whoever/whatever they are, originally lived on Mt Parnassos. The gods then placed Ekhidna-Python-Delphyne in the Korykian Cave to watch over the young Typhoeus/Typhaon and to guard that primordial oracular shrine on behalf of the site's owner.
In his Eumenides the playwright Aeschylus says that the shrine was owned first by Gaia and then by Gaia's daughter Themis and then by Themis' sister Phoibe [Phoebe] who then bequeathed it to her grandson Apollon. In 10.6.6 of his Description of Greece, Pausanias specifically says that Gaia installed Python as the guardian of the place. Hera would then have co-opted Python's services to create a nesting-cave for her Giant dragon-like offspring Typhaon.
This identification and interpretation of Arima is however in disagreement with other ancient writers like Strabo, whose elaborate article on the subject furnishes various alternate explanations. And then of course it circles back to contradict Hesiod because, unlike Python and Delphyne, Ekhidna is explicitly stated in your Theogony quote to be ageless and undying.
