Fine tuning.
1. Save a few bucks flying into DUB, hire a car there and return it there. Better selection of vehicles is also likely.
2. (edited to add you meant The Burren in Clare. My bad.)
3. If, big if, the weather is good the day you drive to Belfast, consider a quick run up to the Giant's Causeway. (Full disclosure I am a massive Led Zeppelin fan and that was the setting for the cover of Houses of the Holy)
youre right about DUB. I just didnt want to drive 3hrs to the cliffs.