The size of Ireland is a common misconception. Some interesting numbers for you, first. At it's widest, Ireland is only 170 miles from coast to coast. The Longest is 301 miles coast to coast, What this translates to, is that you can indeed drive anywhere in Ireland and arrive the same day you leave, although some journeys could be most of the day.
Now that we have it in perspective let's look at those journeys.
Dublin to Kilkenny -: about 85 miles, 2-hour drive.
Kilkenny to Cork -: about 95 miles, 2 hours 15 mins drive
Waterford to Limerick -: about 80 miles, the roads are a little more rural for this journey so the time is still about 2 hours 15 mins.
You can see from the times, a day trip between any of these places is achievable.
Hope this helps you