Odysseus visits a great many places -- most of them not by choice, after he leaves Troy. We first encounter Odysseus on the island of Ogygia, which belongs to the nymph Calypso. He leaves this island on a raft, which Poseidon destroys. Odysseus swims ashore on the island of Scheria, which belongs to the kingdom of the Phaiakans. He goes from Scheria to Phaiakia, where he is welcomed and tells of the many adventures he had before staying with Kalypso.
To the Kikonians drove me the wind that from Ilion bore me,
Ismaros, where I ravaged the city and ruined the people.
...Farther along we sailed from the place; in our hearts we lamented --
glad to flee death as we were -- the destruction of our dear comrades.
Nor would I let my tractable ships go forward before some
crewman had called three times on each of the wretched companions
who died there in the plain, brought down by Kikonian spearmen.
Then at the ships cloud-gathering Zeus set Boreas' stormwinds
raging in furious tempest; (9. 39-40, 62-68)
From the land of the Kikonians, Odysseus' ships are blown for eleven days and nights to the "Lotus-eaters' country" (83-4), where many of his crew wish to stay. Odysseus refuses, and the galleys go on to the land of the Cyclops. There they have the adventure of the Cyclops Polyphemus' cave, in which some of Odysseus' men die. They finally escape, and land on the isle of Aiolia, where they have the adventure of the bag of winds (given them by the king of that country, to speed their return home.) Odysseus' men misunderstand, and open the bag, and they are blown around unmercifully. They return to Aiolia, but the king so disgusted with their irresponsibility he orders them off the island without further assistance.
Six full days we were sailing, alike in the nigt and the daytime;
then on the seventh we came to the high built city of Lamos (10. 80-1)
There, among the Laistrygonians, many of Odysseus' men and ships are lost. Odysseus, in the only ship left, flees to the isle of Aiaia, which belongs to the goddess Circe. There they have many adventures, and they stay there a whole year. From Circe's island Odysseus then goes to the underworld of Hades, where Odysseus sees his mother and the prophet Teiresias, among others. Returning to Circe's island, Odysseus then re-embarks to go home. He passes the obstacles of Scylla and Carybdis, the Sirens, and the cattle of Helios. On the island of Helios, Odysseus' men commit a sacrilege, and Zeus destroys this last remaining ship. Odysseus somehow survives, and he is then washed up on Ogygia, and goes from thence (as described above) to the land of the Phaiakans (where he is now telling his tale.) The kindly Phaiakians then convey Odysseus to his homeland of Ithaka.