Ulysses by James Joyce (1922) is the obvious starting point and the hardest. The entire novel takes place on a single day in Dublin — 16 June 1904 — following Leopold Bloom through the city on foot. Reading it transforms Dublin: suddenly every street has a scene, every pub a character. The first three episodes, set in Sandycove and the bay, are the most accessible entry point. A city map helps.
Dubliners by James Joyce (1914) is the more forgiving introduction: fifteen short stories about ordinary Dublin life, unified by a mood of stasis and escape. "The Dead," the final story, is one of the great short stories in the English language, and its final pages are set on a night when snow is falling across all of Ireland.
At Swim-Two-Birds by Flann O'Brien (1939) is a novel about a Dublin student writing a novel about a man who writes a novel, in which the fictional characters revolt against their author. Savagely funny, encyclopaedically Irish, and unlike anything else. O'Brien's columns in The Irish Times (collected as The Best of Myles) are a good companion read.
Strumpet City by James Plunkett (1969) covers Dublin from 1907 to 1914, centred on the 1913 Lockout — the great labour dispute between trade union leader Jim Larkin and employer William Martin Murphy that shaped the city's character. The best historical novel about Dublin, and essential background for anyone visiting Kilmainham Gaol or the GPO.
Normal People by Sally Rooney (2018) is set partly in Dublin (Trinity College specifically) and partly in Co. Sligo, and captures the texture of young Irish life with uncomfortable precision. Not a guide to the city, but it explains why Trinity students congregate at the Pav.