Seeking help to narrow down and prioritize sights for 9-day itinerary

So, just to let you know, I did not have a car in Ireland, I used a train and bus pass, so I am by no means an expert on driving times, but since nobody else has weighed in, I will express my thoughts on the map you posted. It seems to me that there is a better, more efficient way to do this itinerary that may allow you to add a couple things. You don’t want a car in Dublin, so if you want to see Glendalough you could use a guided day trip, or once you pick up the car drive there, but then carry on from there to Kilkenny. Then from Kilkenny drive to Killarney, stopping at the Rock of Cashel on the way. Do the Ring of Kerry from Killarney, but once you drive the Dingle Peninsula don’t return to Killarney, stay in Dingle or carry on to Limerick if you feel there is something there you want to see. Then drive to Galway stopping at the Cliffs of Moher, Burren etc. along the way. Once you get to Galway you may have another day available to either do a day trip to Inishmore, or drive the Connemara region. Then drive back to Dublin, maybe stopping at Clonmacnoise on the way. This is a pretty full itinerary with lots of one night stands, but I think driving a loop makes more sense than backtracking as it may allow you to see more. Hopefully, some other people will chime in with more experienced comments.

In 9 days, you will only be able to see a small bit of Ireland. The itinerary you give is fine - as long as it covers the places you want to see and the things you want to do there. Killarney makes a good base as there is lots to do and see around there and it has all the requisits a tourist wants. Kenmare would work - it is smaller and less touristy than Killarney but is further to drive for Dingle peninsula and also for Galway. Tralee would also work well and will be less busy than Killarney and is more attractive than Kenmare. It also has the advantage of being closer for Galway... It will take you the full day to drive from Kenmare/Killarney to Galway, particularly if you decide to loop round to see Cliffs of Moher. This only effectively gives you a day for Galway.

Don't underestimnate driving times in Ireland - it will take longer to cover the distances than you might expect. Roads are slow at the best of times and if you get caught up in a traffic off to the races or a funeral, will be a lot slower.

You won't need a car in Dublin, so hire on the day you plan to leave. Think about Rock of Cashel or Cahir on the way to Killarney. Returning to Dublin from Galway, thinks about the medieval town of Athenry with its walls, ruined castle and priory and also the early Christian site of Clonmacnoise with its round towers, ruined chapels and carved crosses.

Thank you for the replies! I was idly wondering about a (quick) visit to Newgrange on the way (though a bit out of the way) back to Dublin from Galway. But considering drive times, a 3:30 PM flight departure, the need to turn in the rental car, etc. that seems quite unrealistic. So thank you for the Athenry suggestion.