The kingdoms (basileis) of mythic Greece only partially coincide with their historical counterparts. What follows is an outline of the Greek kingdoms as they existed in the time of the Trojan War.
The map below is based on the Greek troop catalogue in book 2 of Homer's Iliad, using the towns and geographical landmarks listed to define the various territories. Some of it is guess-work or a rough estimation, especially in the case of the kingdoms of the broad Thessalian plain.
N.B. For Odysseus' kingdom of Ithaca and Meges' kingdom of Dulichium (Doulikhion), I have not followed the Greek geographer Strabo's confused and uncertain identifications of the islands (which has been handed down to the present day). Ithaca, as it is described in the Iliad and the Odyssey, appears to be the western peninsular of the island of Cephallenia--and indeed there are ruins of an ancient Mycenean town beside the harbour. Dulichium is probably the southernmost island now named Zakynthos, and Homer's Zacynthus modern-day Leucas.
The passages quoted below are from Lattimore's translation of the Iliad.
ATTICA & MEGARIS
Transliterations: Attika, Megaris, Athenai
"The men who held Athenai, the strong-founded citadel, the deme of great-hearted Erekhtheus . . . of these men the leader was Peteos' son Menestheus ... Following along with him were fifty black ships." - Homer, The Iliad 2.546
"Out of Salamis Aias brought twelve ships and placed them next to where the Athenian battalions were drawn up." - Homer, The Iliad 2.557
SOUTHERN ARGOS, TROEZEN & AEGINA
Transliterations: Argos, Troizenos, Aigina
"They who held Argos and Tiryns of the huge walls, Hermione and Asine lying down the deep gulf, Troizenos and Eionai, and Epidauros of the vineyars, they who held Aigina and Mases, sons of hte Akhaians, of these the leader was Diomedes of the great war cry, with Sthenelos, own son to high-renowned Kapaneus, and with them as a third went Euryalos, a man godlike, son of Mekisteus the king, and scion of Talaos; but the leader of all was Diomedes of the great war cry. Following along with these were eighty black ships." - Homer, The Iliad 2.559
NORTHERN ARGOS, CORINTH & SICYON
Transliterations: Argos, Korinthos, Sikyon, Mykenai
"The men who held Mykenai, the strong-founded citadel, Korinthos the luxurious, and strong-founded Kleonai; they who dwelt in Orneai and lovely Araithyrea, and Sikyon, where of old Adrestos had held the kingship; they who held Hyperesia and steep Gonoessa, they who held Pellene and they who dwelt about Aigion, all about the sea-shore and about the wide headland of Helike, of their hundred ships the leader was Agamemnon." - Homer, The Iliad 2.569
"They who held the swarming hollow of Lakedaimon, Pharis, and Sparta, and Messe of the dove-cotes, they who dwelt in Bryseiai and lovely Augeiai, they who held Amyklai and the seaward city of Helos, they who held Laas, and they who dwelt about Oitylos, of te=hse his brother Menelaos of the great war cry waws leader, with sixty ships marshalled apart from the others." - Homer, The Iliad 2.581
Messenia sent no independent contingent to the Trojan War. The presumed heirs to the throne of Messenia were the twins Idas and Lynkeus who were slain by the Dioskouroi just prior to the War. The kingdom may have then been incorporated into that of King Nestor's neighbouring Pylos.
"They who dwelt about Pylos and lovely Arene, and Thryon, the Alpheios crossing, and strong-built Aipy; they who lived in Kyparisseeis and Amphigeneia, Pteleos and Helos and Dorion ... the leader was the Gerenian horseman, Nestor, in whose command were marshalled ninety hollow vessels." - Homer, The Iliad 2.592
"They who held Arkadia under the sheer peak, Kyllene, beside the tomb of Aipytos, where men fight at close quarters, they who dwelt in Orkhomenos of the flocks, and Pheneos, about Rhipe and Stratia and windy Enispe; they who held Tegea and Mantineia the lovely, they who held Stymphalos, and dwelt about Parrhasia, their leader was Angkaios' son, powerful Agapenor. Sixty was the number of their ships, and in each ship went many men of Arkadia, well skilled in battle." - Homer, The Iliad 2.603
"They who lived in Bouprasion and brilliant Elis, all as much as Hyrmine and Myrsinos the uttermost and the Olenian rock and Alesion close between them, of these there were four chieftains, and with each man ten swift vessels followed, with many Epeian men on board them. Of two tens Thalpios and Amphimakhos were leaders, of Aktor's seed, sons one of Kteatos, one of Eurytos. Ten more were led by Amaryngkeus' son, strong Diores, and of the fourth ten godlike Polyxeinos was leader, son of lord Agasthenes, of the race of Augeias." - Homer, The Iliad 2.615
The kingdom of Olenos was conquered by the Aitolians just prior to the Trojan War and so its troops participated as a part of the Aitolian contingent.
Transliterations: Euboia, Khalkis
"They who held Euboia, the Abantes, whose wind was fury, Khalkis, and Eretria, the great vineyards of Histiaia, and seaborne Kerinthos and t he steep stronghold of Dion, they who held Karystos and they who dwelt about Styra, of these the leader was Elephenor, scion of Ares, son of Khalkodon and lord of the great-hearted Abantes. And the running Abantes followed with him, their hair gown long at the back, spearmen furious with the outreached ash spear... Following along with him were forty black ships." - Homer, The Iliad 2.536
Transliterations: Locris, Opus
"Swift Aias son of Oileus led the men of Lokris, the lesser Aias, not great in size like the son of Telamon, but far slighter ... These were the dwellers in Kynos and Opoeis and Kalliaros, and in Bessa, and Skarphe, and lovely Augeiai, in Thronion and Tarphe and beside the waters of Boiagros. Following along with him were forty black ships of the Lokrians, who dwell across from sacred Euboia." - Homer, The Iliad 2.527
Transliterations: Minyai, Orkhomenos
"But they who lived in Aspledon and Orkhomenos of the Minyai, Askalaphos led these, and Ialmenos, children of Ares ... With these two there were marshalled thirty hollow vessels." - Homer, The Iliad 2.511
"Leitos and Peneleos were leaders of the Boiotians, with Arkesilaos and Prothoenor and Klonios; they who lived in Hyria and in rocky Aulis, in the hill-bends of Eteonos, and Skhoinos, and Skolos, Thespeia and Graia, and in spacious Mykalessos; they who dwelt about Harma and Eilesion and Erythrai, they who held Eleon and Hyle and Peteon, with Okalea and Medeon, the strong-founded citadel, Kopai, and Eutresis, and Thisbe of the dove-cotes; they who held Koroneia, and the meadows of Haliartos, they who held Plataia, and they who dwelt about Glia, they who led the lower Thebes, the strong-founded citadel, and Onkhestos the sacred, the shining grove of Poseidon; they who held Arne of the great vineyards, and Mideia, with Nisa the sacrosanct and uttermost Anthedon. Of these there were fifty sips in all, and on board each of these a hundred and twenty sons of the Boiotians." - Homer, The Iliad 2.494
Transliterations: Phokis, Krisa
"Skhedios and Epistrophos led the men of Phokis, children of Iphitos, who was son of great-hearted Naubolos. They held Kyparissos, and rocky Pytho, and Krisa the sancrosanct together with Daulis and Panopeus; they who lived about Hyampolis and Anamoreia, they who dwelt about Kephisos, the river immortal, they who held Lilaia beside the well springs of Kephisos. Following along with these were forty black ships, and the leaders marshalling the ranks of the Phokians set them in arms on the left wing of the host beside the Boiotians." - Homer, The Iliad 2.511
Dryopia (the region later known as Ozolian Lokris) did not contribute any troops to the Trojan War. The kingdom was ruled by the Herakleidai (sons of Herakles) at the time of the War - see Thessalian Doros below (which was their main holding).
Transliterations: Aitolia, Kalydon
"Thoas son of Andraimon was leader of the Aitolians, those who dwelt in Pleuron and Olenos and Pylene, Kalydon of the rocks and Khalkis beside the sea-shore, since no longer were the sons of high-hearted Oineus living, nor Oineus himself, and fair-haired Meleagros had perished. So all the lordship of the Aitolians was given to Thoas. Following along with him were forty black ships." - Homer, The Iliad 2.638
CEPHALLENIA, ITHACA & ZACYNTHUS
Transliterations: Kephallenia, Ithaka, Zakynthos
"Odysseus led the high-hearted men of Kephallenia, those who held Ithaka and leaf-trembling Neriton, those who dwelt about Krokyleia and rugged Aigilips, those who held Zakynthos and those who dwelt about Samos, those who held hte mainland and the places next to the crossing. All thse men were led by Odysseus, like Zeus in counsel. Following with him were twelve ships with bows red painted." - Homer, The Iliad 2.631
"They who came from Doulikhion and the sacred Ekhinai islands, where men live across the water from Elis, Meges was the leader of these, a man like Ares, Phyleus' son, whom the rider dear to Zeus had begotten, Phyleus, who angered with his father had settled Doulikhion. Following along with him were forty black ships." - Homer, The Iliad 2.625
Thesprotia did not send any troops to the Trojan War. It was ruled by Queen Kallidike at the time.
MALIS, PHTHIOTIS & DOLOPIA
Transliterations: Malis, Phthiotis, Trakhis
“Now all those who dwelt about Pelasgian Argos, those who lived by Alos and Alope and at Trakhis, thos who held Phthia and Hellas the land of fair women, who were called Myrmidones and Hellenes and Akhaians, of all these and their fifty ships the lord was Akhilleus.” - Homer, The Iliad 2.681
“They who held Phylake and Pyrasos of the flowers, the precinct of Demeter, and Iton, mother of sheepflocks, Antron by the sea-shore, and Pteleos deep in the meadows, of these in turn fighting Protesilaos was leader while he lived … Yet these, longing as they did for their leader, did not go leaderless, but Pokarkes, scion of Ares, set them in order, child of Iphikles, who in turn was son to Phylakos rich in flocks, full brother of high-hearted Protesilaos.” - Homer, The Iliad 2.695
"They who lived by Pherai beside the lake Boibeis, by Boibe and Glaphyrai and strong-founded Iolkos, of their eleven ships the dear son of Admetos was leader, Eumelos, born to Admetos by the beauty among women Alkestis, loveliest of the daughters of Pelias." - Homer, The Iliad 2.711
"They who lived about Thaumakia and Methone, they who held Meliboia and rugged Olizon, of their seven ships the leader was Philoktetes ... yet he himself lay apart in the island, suffering strong pains, in Lemnos the sacrosanct, where the sons of the Akhaians had left him in agony from the sore bite of the wicked water snake ... Yet these did not go leaderless, but Medon, the bastard son of Oileus, set them in order, whom Rhene bore to Oileus the sacker of cities." - Homer, The Iliad 2.716
Transliterations: Phlegyai, Trikke
"They who held Trikke and the terraced place of Ithome, and Oikhalia, the city of Oikhalian Eurytos, of these in turn the leaders were two sons of Asklepios, good healers both themselves, Podaleirios and Makhaon. In their command were marshalled thirty hollow vessels." - Homer, The Iliad 2.729
"They who held Ormenios and the spring of Hypereia, they who held Asterion and the pale peaks of Titanos, Eurypylos led these, the shining son of Euaimon. Following along with him were forty black ships." - Homer, The Iliad 2.734
At the time of the Trojan War the kingdom of Doros was ruled by the Herakleidai (sons of Herakles). They did not take part in the Trojan War since the Heraklid suitor of Helene, Tlepolemos, had been exiled to the island of Rhodes.
Transliterations: Lapithai, Gyrtone
"They who held Argissa and dwelt about Gyrtone, Orthe and Elone and the white city of Oloosson, of these the leader was Polypoites, stubborn in battle, son of Peirithoos whose father was Zeus immortal, he whom glorious Hippodameia bore to Peirithoos on that day when he wreaked vengeance on the Pheres [the Centaurs] and drove them from Pelion ... Following in the guidance of these were forty black ships." - Homer, The Iliad 2.738
Capital: Cyphus, Dodona
Transliterations: Perrhaibia, Kyphos, Dodona
"Gouneus from Kyphos led two and twenty vessels, and the Enienes and the Perrhaibians stubborn in battle followed him, they who made their homes by wintry Dodona, and they who by lovely Titaressos held the tilled acres, Titaressos, who into Peneios casts his bright current: yet he is not mixed with silver whirls of Peneios, but like oil is floated along the surface above him." - Homer, The Iliad 2.748
"Prothoos son of Tenthredon was leader of the Magnesians, those who dwelt about Peneios and leaf-trembling Pelion. Of these Prothoos the swift-foted was leader. Following along with him were forty black ships." - Homer, The Iliad 2.756
Pieria did not send any troops to the Trojan War. The country was usually described in myth as a non-Greek land ruled by Thrakian kings.
Transliterations: Krete, Knossos
"Idomeneus the spear-famed was leader of the Kretans, those who held Knosos and Gortyna of the great walls, Lyktos and Miletos and silver-shining Lykastos, and Phaistos and Rhytion, all towns well established, and other who dwelt beside them in Krete of the hundred cities. Of all these Idomeneus the spear-famed was leader, with Meriones, a match for the murderous Lord of Battles. Following along with these were eighty black ships." - Homer, The Iliad 2.645
Transliterations: Rhodos, Lindos
"Herakles' son Tlepolemos the huge and mighty led from Rhodes nine ships with the proud men of Rhodes aboard them, those who dwelt about Rhodes and were ordered in triple division, Ialysos and Lindos and silver-shining Kameiros." - Homer, The Iliad 2.653
"Nireus from Syme led three balanced vessels, Nireus son of Aglaia and the king Kharopos, Nireus, the most beautiful man who came beneath Ilion." - Homer, The Iliad 2.671
COS, NISYRUS, CARPATHUS, CASOS
Transliterations: Kos, Nisyros, Karpathos, Kasos
"They who held Nisyros and Krapathos and Kasos, and Kos, Eurypylos' city, and the islands called Kalydnai, of tehse again Pheidippos and Antiphos were the leaders. In their command were marshalled thirty hollow vessels." - Homer, The Iliad 2.676
Melos sent no troops to the Trojan War. Its king at the time was Polyanax.
Delos sent no troops to the Trojan War. Its king at the time was Anios.
Lemnos sent no troops to the Trojan War. Its king at the time was Euneus.
Skyros sent no troops to the Trojan War. Its king was Lykomedes who had Akhilleus' son Neoptolemos in his care. The island was probably merely a vassal of Malis-Pthiotis.
SAMOS, CHIOS, NAXOS, PAROS, SAMOTHRACE, THASOS
Transliterations: Khios, Samothrake
None of these island kingdoms participated in the Trojan War.