Lots of good ideas here--I agree that there is plenty to do in each area. Remember that you really will have no time for anything other than breakfast on the 18th if you are getting to the airport for a noon international trip.
I like the idea of heading to Galway on public transit that first day. The Connemara Loop was lovely. I still regret not purchasing a print at the Whitethorn gallery in Clifden.
We loved Kilkenny, a very doable day trip from Dublin, although staying a night or two provides some time to relish the atmosphere. (We loved Mena House BnB, a hefty walk from town.) The Boyne Valley/Newgrange was really fascinating, so could be added if you based in Dublin an extra day, or had a car on the way to Galway. We went to Knowth on one trip and Newgrange on another (flight was delayed, so first trip we could only do one before heading north for our reservations)
We also really liked our time on the Dingle penisula and environs, but maybe put Dingle/Killarney, Cliffs of Moher on a future wish list. Frankly, I found the Buren more to my interest than the Cliffs. All would make a good future visit.
Any extra days allotted to Dublin would allow for day trips, as mentioned. For only 9 days, the least amount of accommodation shuffle will allow more time to enjoy.
Our first trip to Ireland was about 10 days. We covered a lot of ground by car, loved it, but wish we'd had a little more time to absorb each location. (We were also 15 years younger.) We rented a car at the airport, went to Knowth, (before delayed flight we had a night scheduled outside Knowth) headed up to Donegal County where we were based for a few days, drove down to Dingle with a couple of nights along the way. We flew from Cork to England for a few days before flying home to Washington. Our 2nd trip was closer to 3 weeks.