Most Ireland itineraries are lists of places. The better unit is bases: towns you sleep in for several nights and drive out from. Get the bases right and the rest of the trip largely plans itself.
Dublin
Where most people land. Two nights is standard, one is defensible if you are short, and four is only worth it if you like cities. Stay within the canals — Dublin 2, 4, 6 or 8 — rather than at an airport hotel, and you can walk almost everything.
Within an hour: Glendalough, the Wicklow Mountains, Newgrange, Howth.
Kilkenny or Cork
The natural first stop heading south or west. Kilkenny is smaller, medieval and walkable in an evening. Cork is a real city with the best food scene in the country and a harbour worth a day.
Within an hour of Kilkenny: the Rock of Cashel, Waterford, the Copper Coast. Within an hour of Cork: Kinsale, Cobh, Blarney, the start of the Beara road.
Killarney or Dingle
The Kerry decision, and the one people most often get wrong. Killarney is bigger and better connected. Dingle is smaller and better.
Killarney puts the national park, the Ring of Kerry and the Gap of Dunloe within reach, and has the beds and restaurants a busy town needs. Dingle is an hour further west, has a harbour, a distillery and the Slea Head drive on its doorstep, and feels like somewhere people actually live.
If you have three nights in Kerry, do two in Dingle and one in Killarney. If you have one, make it Dingle.
Galway
The best base in the country for range. Connemara, the Burren, the Cliffs of Moher, the Aran ferries and Clare are all inside ninety minutes. The city itself is small enough to walk and has the music.
Three nights in Galway covers more ground than three nights anywhere else in Ireland.
Westport, Sligo or Donegal
Only if you have a fortnight. Westport is the prettiest town in Mayo and the gateway to Achill. Sligo has Ben Bulben and Yeats country. Donegal is the wildest coastline in Ireland and the county most often cut for time and most often regretted.
Belfast
Ninety minutes from Dublin on the motorway and skipped by most itineraries. Two nights covers the city, the Titanic Quarter and a day on the Causeway Coast, which is the equal of anything in the Republic.
Putting it together
A fortnight that works: Dublin 2, Kilkenny or Cork 2, Dingle 3, Galway 3, Belfast 2, with two nights spare for weather or the place you fall for. Five hotels in fourteen nights. That is the shape.