Do I need to hire a car?
In Dublin, no: walk, use the Luas tram and the buses, and take a train or a tour for day trips. For rural Ireland, a car is close to essential. The places people cross an ocean for, the peninsulas, the small towns, the coast roads, are served thinly by buses. If you would rather not drive, base yourself in two or three towns and use local tours for the countryside days.
Useful pages: Itineraries · The best time to visit Ireland · What to wear