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Eustace in the Steps of Nald at X12-Y9 wants to introduce you to levequests. He'll ask you to speak with Totonowa at Horizon, which is at X23-Y16 in Western Thanalan. Totonowa will set you up with a Guildleve called What Peistes Crave. Accept the Levequest, then head to X18-Y16 and initiate the quest (Press "J" to open your journal, click the Levequest, then click Initiate).
Slay the Softskin Peiste, then return to Totonowa to complete the quest and unlock City-Stay Levequests.