Why does Telemachus go to Pylos and Sparta?

Telemachus goes to Pylos and Sparta to seek news of his father, Ulysses, and to gain advice from the wise men of Pylos and Sparta on how to deal with the suitors who have been harassing his mother and taking advantage of his father's absence. He visits Nestor in Pylos and Menelaus in Sparta, both of whom had been close friends of Ulysses. He hopes to gain insight into Ulysses' whereabouts and gain advice on how to handle the suitors from these two wise men. He is also encouraged by the goddess Minerva to seek out news of his father and to gain advice from the wise men of Pylos and Sparta. Additionally, Telemachus is driven to seek out news of his father and gain advice from the wise men of Pylos and Sparta due to the taunting of the suitors, who suggest that he will bring friends to help him from Pylos or Sparta, or even go to Ephyra for poison to put in their wine and kill them. He also hopes to find out what happened to his father, as the suitors suggest that he may have perished far from his friends.

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“I did not think of asking about that,” replied Eumaeus, “when I was in the town. I thought I would give my message and come back as soon as I could. I met a man sent by those who had gone with you to Pylos, and he was the first to tell the news to your mother, but I can say what I saw with my own eyes; I had just got on to the crest of the hill of Mercury above the town when I saw a ship coming into harbour with a number of men in her. They had many shields and spears, and I thought it was the suitors, but I cannot be sure.” On hearing this Telemachus smiled to his father, but so that Eumaeus could not see him. Then, when they had finished their work and the meal was ready, they ate it, and every man had his full share so that all were satisfied. As soon as they had had enough to eat and drink, they laid down to rest and enjoyed the boon of sleep.

Telemachus went through, and out of, the cloisters spear in hand—not alone, for his two fleet dogs went with him. Minerva endowed him with a presence of such divine comeliness that all marvelled at him as he went by, and the suitors gathered round him with fair words in their mouths and malice in their hearts; but he avoided them, and went to sit with Mentor, Antiphus, and Halitherses, old friends of his father’s house, and they made him tell them all that had happened to him. Then Piraeus came up with Theoclymenus, whom he had escorted through the town to the place of assembly, whereon Telemachus at once joined them. Piraeus was first to speak: “Telemachus,” said he, “I wish you would send some of your women to my house to take away the presents Menelaus gave you.”