Itinerary Critique - End of May 2018

Suggest staying an extra night in Kenmare to more thoroughly explore the ROK, then make Cashel (and/or Kilkenny) an enroute stop on your way to Dublin.
Either driving to Galway or taking the train and renting a car upon arrival are good options. Comes down to personal preference really. If you'd like to make any stops along the way then the car is obviously preferable. If you just want to "get there" then take the train.
Would recommend making it a day trip to Inish mor, if only to free up a day to drive the exquisite Connemara Loop...Clifden, the Sky Road, the National Park, Kylemore Abbey, Cong, etc.

If you're In a hurry to do things in the Galway area a train. If you have time a car is wonderful for fun stops big and small along the way.

Just personal preference but three nights in Galway I would much rather spend in other places. Galway is pretty but it is a city......congested and touristy.....and after three days in Dublin you are getting lots of 'city'. Really depends on what you want. It is an excellent idea to pick a base for a few days and explore from there. I would ad time especially to the ROK. You can drive it in a day but you will miss so much racing around it.....and it will be a long car day. Missing the Skellig Ring and so many interesting spots along the ROK is a shame. Galway IS a good option as a base....but there are better, unless you really prefer a city environment......and if so Galway is excellent for that.

A day trip to the Arans is doable but because of sailing times spending just one night there doesn't ad much exploring time and kills another day. It is really worth a day trip though. Dun Anghosa and the cliffs, and views are fantastic.

Hope while in Dublin you aren't in the city all three days and can take day trips from there.....Newgrange and especially Wicklow - Glendalough are fantastic.

With limited time trade offs are necessary.....So while Cashel is a fun spot to visit, very impressive, I'd skip it for more time in the ROK/Skellig Ring area. Less really is more. Ending the trip with reasonably calm time in the spectacular southwest is a great way to cap things off. The people there are especially great and having the time to interact a bit is worth trimming a day or two elsewhere.

Hope you have a great trip !!

Thank you both for responding. My wife and I will take these suggestions under consideration and retool our plans. As I noted, we were planning to use Galway as a base for 3 nights we'd be staying there, but maybe there is a better location perhaps in County Clare, like Ennis. Also, approximately how long (either mileage of appropriate drive time) for the Connemara Loop?

We are going back in April and will be using Galway as our base for 3 nights, which we have done on several prior trips. Our preference is to stay in Salthill and take a bus into the city (or walk in and bus back, depending on the location of our B&B.)

3 nights in a location really only gives you 2 full days. Use the afternoon of your arrival day to explore the city. The city center is very compact and fun to walk, but a pain to drive in, and it can be hard to find a place to park.

Driving through Connemara can take a few hours or a full day or more, depending on your travel style and what you would like to see. We like to go out via Barna and Spiddal, take the loop down to Roundstone, then on to Clifden. (Be sure to drive Sky Road here for some great sights.) Do you want to visit Kylemore Abbey? Cong? Plan to make lots of stops to take photos! Hope it’s a great trip.

Per AlliM, how long the Connemara Loop will take will be entirely up to you. In our case it takes most of a full day, but we typically meander and take our time at the various stops.
There are pleasant walks in the National Park that can require a couple of hours. One in particular up Diamond Hill features beautiful views on a sunny day. Clifden and the Sky Road are worth exploring at your leisure, as is Kylemore Abbey. If you're a fan of "The Quiet Man" - the old John Wayne/Maureen O'Hara film from the 1950's - you'll want to spend a couple of hours in the cute little town of Cong just scouting out all of the film locations. Ashford Castle is there too.
Add the fact that you'll be driving on rural roads and can therefore disregard the estimated drive times you'll see on Google Maps, and you have the makings of what is easily an all day excursion ... one of the most pleasant and scenic in Ireland in our opinion. Fact is that after a dozen visits to the country we still make it a point to revisit on every trip.