Dublin to Killarney? To Galway

Since they'll already be at Dublin airport upon arrival, they could just stay there after collecting their bags and hop on the morning RyanAir flight which departs at 10:05 AM to the Kerry airport near Killarney. Would save a half day's travel versus doing it by train.
Killarney is probably the best bet for a base - it's central to pretty much everything and is the hub for all of the day tours.
Getting from Killarney up to Galway would need to be by bus via Limerick but it looks pretty straightforward.
Galway is then a good base for day trips and tours around the area - including the trip out to the Aran islands. The ferry crossing can be rough if the sea states kick up. Another option would be to fly - which doesn't cost much more than the ferry. https://aerarannislands.ie/
That would streamline their logistics somewhat and allow them to enjoy Dublin at the end of the trip.

You can get nearly anywhere in Ireland by public transportation. Here is the map of where the trains go:
https://www.seat61.com/reference/Ireland-map.pdf?dl=0
Transport for Ireland has comprehensive transport information, route planner, etc.:
https://www.transportforireland.ie
Cycle hire is very available, as well.
Of course, Paddywagon and others offer all-day bus tours, but these are expensive for what they offer.
At this late stage, they may be limited by where they can get a room. Here is information about youth hostels in Ireland:
https://www.ireland.com/en-us/plan-your-trip/accommodation/hostels-in-ireland/
There is a hostel on one of the Aran Islands.
There is also a hostel near the Skelligs in Kerry, where there is also bioluminescence. Probably more accessible than Lough Hyne? I don't know. It's not my bag.

You say they want to be off the beaten path, yet you are sending them on the beaten path (except, notably, the Cliffs of Moher), Killarney being the most beaten of paths in Ireland. If they want to go kayaking and visit sea caves, they should go where those things are.
Here is a site called Caves of Ireland:
https://cavesofireland.com
It sounds like they enjoy the outdoors and want to see the natural beauty of Ireland. Take a look at Doolin to see if you can find affordable accommodation. There is good access to Aran Islands, Cliffs of Moher, the Burren and sea caves from Doolin. Lots of Forum folks stay there because there is a lively traditional music scene. Here is the tourism website: https://doolin.ie
Because it's a very touristic town, it might be hard to find something affordable. Try nearby towns and villages and double check for transport links.

Thanks so much for the pointers, everyone! Looking into them all!

Agree that they are staying in commonly visited areas, but they have to stick to where public transportation can take them and where I could find stays in hostels. I wish I could find something in Doolin!

I was thinking a bunch of day trips from the "central" areas they are staying in, and then only spending evenings in the towns/cities of Killarney and Galway.

Has anyone done Pigeon Hole in Cong? Maghera Beach in Ardara?

You didn't mention that you had already booked accommodation. I recommend searching this site for "day trips from Galway" since that is what you are actually looking for. Or you could let the travelers figure it out.

Take a look at the "Things to Do" menu on Trip Advisor. A cursory check turned up a number of day trips and tours that might be of interest.

Another great resource will be the staff and guests at the hostel.