Ireland's latitude is roughly between the 52nd and 55th parallels, thus, theoretically, the whole country is good to see northern lights. However, in reality, that happens rarely. Big cities experience light pollution, so if you are a northern lights chaser, you'd want to go as far out as possible and, of course, further north.
Donegal County is one of the most popular destinations. Tra na Rossan Beach on the Rosguill Peninsula has a good location and little light pollution along the northern headlands. Inishowen Peninsula offers a few excellent spots for viewing northern lights. One of them is Malin Head, a great place to see aurora borealis thanks to its northernmost location in the country. Another one is Dunree Head that also offers the Dunree Fort as a shelter and a museum alongside several nature walks and a picturesque bay to be explored during the day.
The Mullet Peninsula and the town of Belmullet with its two bays, Blacksod Bay and Broadhaven Bay, is a well-known northern lights gazing spot. The Glencolumbkille on the Slieve League Peninsula is also lucky to experience the phenomenon.
The northern lights are hard to predict however your best chance in Ireland is usually from 9 p.m. to 1 a.m. during the period from September through March. The equinoxes usually have more frequent auroras.