If you want to see the whole of Ireland then I’d suggest visiting for 10 days, but preferably two weeks. In 10 days you can cover a lot of places in both Northern and Southern Ireland but your itinerary will be jam-packed. With two weeks you can do things at a more leisurely pace. Obviously if you don’t have that kind of time then you could just spend a day or two in Dublin and then possibly do a day trip to Galway or Wicklow.