Consider putting Dublin at the end. You will not be jet-lagged so hire the car and get on the road from the airport rather than a couple of days in the city back north to the airport to go south again?

Powerscourt and or Glendalough to Killarney for one night.

Cashel and Cahir before the second night around Cork (Blarney is a fair option)

You have the option of driving round Beara to Kenmare or heading to Killarney and explore the National Park a little, night three.

Ring of Kerry is overrated unless you have a couple of days to explore so give that a miss? There is a compulsion that every visitor must drive round Dingle. If you miss out the Ring of Kerry consider Dingle for night four (I didn't suggest that if anyone asks, have a reputation to keep)

Take the main road through the Shannon Tunnel and head to the Clare coast from below Ennis (you could call at Bunratty Folk park first) and aim for the Cliffs or Doolin. You can take a cruise under the cliffs from Doolin. Maybe the Hawk walk at Allwee caves by Ballyvaughan. and a night out in Galway.

Over the M6 eastwards for your Newgrange visit (Drogheda?) drop the car at the Airport whilst north of the city.

You don't really need the car in the city, there are good buses in and out to the airport.

A tool I found useful on my two driving trips in Ireland was the AA Route Planner. It should help you decide how far you can reasonably drive in a day. Just be sure to add about 20% to the stated driving times. Just as in New Zealand, many of the Irish roads aren't meant to be driven quickly despite the posted limits.

http://routes.aaireland.ie/

Also, while you should be able to find accommodations along the road, even in summer, (unless there's a festival going on), you may not be able to get your first choice. If you aren't choosey about where you stay, you'll be fine.

Planning a trip to Ireland in September. We are not interested in big cities - want to be spontaneous yet there are some sights we definitely want to see. Any DO NOT MISS or DON'T BOTHER is helpful. Also, any B&B recommendations, etc. are appreciated. Below is a possible route. Is this feasible? Would someone be so kind as to give me feedback.
Day 1 = Early arrival into Dublin. Take tour of area....spend night
Day 2 - Leave early drive to Antrim Coast north of Belfast, spend night on Antrim Coast
Day 3 - Travel north/northwest - Giants' Causeway, Dugliven (searching for family cemetery), Londonderry, Ulster Folk Park -spend night in Donegal
Day 4 - Donegal toward Ballyshannon, Sligo,spend night West Mayo
Day 5 - Travel and see Cliffs of Moher, Aran Islands other sights on way to Doolin...spend night outside Doolin
Day 6 - Travel to Killarney - sights along the way. Spend night in Killarney
Day 7 - Dingle Penisula - spend night in same B & B in Killarney
Day 8 - Ring of Kerry....then on to Kinsale - spend night in Kinsale
Day 9 - Cork Area - Rock of Cashal...spend night in Kilkenny
Day 10 - Wicklow Mts., Gardens of Powercourt
spend night in Dublin
Day 11 - Return home to the USA