In more specification I am looking for what cities existed at the time and what political entities held influence on Corsica and surrounding islands in roughly 480 BCE. I understand Carthage held control over part of the island at the time but I would like more detail on that. Did they hold subject states in the region or was it more of a direct rule? Information on this and sources that could be used to research this would be much appreciated.
Corsican Iron Age is not much known, and that's only very recently that an archaeological and historical interest was given in the period, divided between a First and a Second Iron Age by the foundation of the Greek settlement of Alalia in the VIth century BCE : the knowledge on indigenous and colonial societies thus suffers in comparison to mainland archeological and historical understanding.
The indigenous populations were likely the descendants of the Torrean culture, itself materially close to Nuragic Sardinia, but their relation to mainland peoples is not clear : the "Ligurian" epithet which is still sometimes present in vulgarization not only wasn't used as such by ancient authors on the insular population but was probably more of a geopolitical concept, a coastal band where indigenous and settlers directly interacted; although toponimical roots (-a/osco, -inco or -elu) found in Alpine France and Italy are present in Corsica as well, which remains to be decisively interpreted.
A priori, local dynamics were proper to the island, without a significant connection to their southern neighbor, which is not wholly absent either.
The island is archeologically divided between a southern and a northern ensemble. Meridional communities giving up most of the defensive apparatus, relatively apart from Mediterranean exchanges until the VIIth century BCE, with small Sardinian products finding their way in, until an archeologically attested presence of Punic/Ibero-Punic beads or Greek transportation pottery. The northern region's transformation of the habitat is less pronounced and is more associated with an earlier participation to Thyrrenian trade, especially in regards to local elites displaying jewelry and metallic tableware, along with local metal working (and possibly mining).
Etruscan presence in Corsica, besides the proximity of Italy, likely took the form of seasonal or even permanent presence of individuals or communities in the island which we have little traces of for the First Iron Age in spite of Etruscan products found in indigenous, often ostentatory, context.
These contacts likely took the form of seasonal, or possibly permanent in the case of Etrurscans, presence of traders along the coast, where indigenous populations and foreign sailors interacted. There is, however, no traces of settlement in Corsica comparable to the Punic or Greek foundations in Sardinia such as Tharras or Calaris. Along the Mediterranean shores, the make-up of exclusive trade networks wasn't that achieved yet by the VIth century, Carthaginians eventually pushing back Grees out of the western third of the Mediterranean basin.
Alalia (Aléria/Aleria), might have been such an emporion before it was tentatively settled by Phoceans in the mid-VIth century BCE which, according to Herodotos, were fleeing Phocea to avoid the Persian conquest of the city. This foundation was short-lived, leaving no archeological evidence, and the inconclusive Battle of Alalia, against a Puno-Etruscan coalition, did not as much forced Greeks out of the island (their presence can still be hinted at in the southern regions) but prevented the perpetuation of a quasi-exclusive presence as with southern-eastern Gaul : Alalia, whose relationship with indigenous communities is difficult to assess, gives the impression of an emporion whose political influences over the island were null.
Eventually, during the Greco-Persian wars, Corsica wasn't much under anyone's authority : we don't know much about indigenous polities, even if the settlement pattern could hint at being based on overseeing mountainous valleys, but neither Carthaginian or Etruscan presence took the form of an actual coastal control we'd know about archeologically or historically for the period As it happened for the Mediterranean Iron Age in Spain, Gaul or Spain, the coastal area was much less a controlled area than an accosted area where locals and traders, and eventually settlers, directly interacted with each other.
Unfortunately, we know little about these interactions : Diodorus Siculus mentions that Corsicans gave Greeks a tribute of honey, resin and wax (V, 13) but his account there might be problematic as he erroneously locates Calaris (Cagliari) in Corsica, unless both Calaris and Nikaia were outpost founded or controlled by Syracuseans over the IIIrd century BCE (further mentioned, XI, 88), Diodorus then antedating situation from there to the VIth century BCE.
Eventually, there's no real evidence of a Carthaginian, even partial or coastal, control in Corsica for most of the insular Iron Age until they expelled Syracusans out of the island.