Good base for country day trips

Will you have a car?

Yes, although a bit nervous about driving g on the other side of the road we realize it will be easier to hire a car for rural sightseeing.
Susan

We enjoyed Kenmare which is less busy and touristy than Killarney and a good base. We also liked County Galway and Connemara. If you don't want to stop in Galway, there are places like Clifden.

Given the high cost of rental cars at the moment you'd be well advised to try and minimize the time you actually need one.
One strategy would be to stay in Dublin for several nights at the beginning of your trip - both to shed the effects of jet lag and to take advantage of being in the transportation hub for potential day trips by train to Belfast and Kilkenny, There are a number of day trip and tour providers based in Dublin for trips north to Newgrange and the Boyne Valley and south to Glendalough, Powerscourt and the Wicklow Mountains. You wouldn't need a car for any of that.
Once you've satisfied your curiousity about Dublin you could catch a train or bus over to Galway for a few nights, taking organized day tours from there over to the Aran Islands and the beautiful Connemarra region - again, no need for a car just yet.
You could then pick up a rental car as you depart Galway for a leisurely drive down the coast towards Dingle and Kerry ... for which you'll really need a car to enjoy the area to best advantage.
Most here recommend avoiding Killarney town. Though it appears to be a great base on the map the fact is that it tends to be a congested mess when the tour buses are rolling - which is most of the time. For a single base to explore both the northern part of the ROK and Dingle consider staying somewhere along the corridor between Glenbeigh and Castlemaine. You could unpack once for a week or so and enjoy some of the prettiest scenery in Ireland at your leisure and without the crowds of high season. Dingle town and the peninsula, the Gap of Dunloe, Killarney National Park and the exquisite Skellig Ring Road would be less that an hour's drive away.
Kenmare is a good choice as a base along the southern part of the ROK as well as being a convenient jumping off point for excursions out to the Beara peninsula immediately south where you'll find some of the best hiking in Ireland along the Beara Way.
Once you've completed your stay in the area you could drop your rental car at the Kerry airport near Killarney and catch one of the two flights per day on RyanAir back to Dublin for your return flight home. With rental cars going for over $100 per day that approach might save you some money while still providing maximum flexibility for rural excursions in the west of Ireland.

Thanks so much for the tips, it’s been really helpful. 🤓