Tips on good home base west coast Ireland

Dingle, Kilarney, Kinsale

Having a car Killarney would be my choice although a lot of tourists in summer month

But you can do day tours from there to the Dingle Peninsula the Ring of Kerry and Skelligs Ring the Beara Peninsula
and of course the Killarney National Park.

https://theringofkerry.com/

Dont know if you like to stay in a Holiday Home or prefer Hotel Guesthouse B+B accomodation.
All available in and near Killarney town but also on the Iveragh Peninsula in more remote areas.

I can post some links if you like. You tell what kind of accomodation you prefer

Another town to go from Killarney and stay there for a few days is Schull on the Mizen Peninsula

http://www.schull.ie/

Explore the Mizen Peninsula from there

https://www.discoveringireland.com/mizen-head-peninsula/

see
Barley Cove Beach

https://www.theirishroadtrip.com/barleycove%E2%80%8C-%E2%80%8Cbeach%E2%80%8C-%E2%80%8Cin%E2%80%8C-%E2%80%8Ccork/

and
Mizen Signal Station

https://mizenhead.ie/

or
do some whale watching (35km from Schull)

https://www.baltimore.ie/whale%20watching

or daytours to

Bantry and Bantry House (30 km from Schull)

https://www.bantryhouse.com/

or
the Sheepshead Peninsula

https://thesheepsheadway.ie/

Btw
Schull and Baltimore are on the way to the above mentioned Kinsale in West Cork from Killarney

Kenmare was my base for 3 days in May 2023 and it and allowed for very doable trips to Killarney NP, ROK, Beara Penninsula, SW Ireland. Drove to Killarney and found it very congested. Kenmare was busy but more manageable as it is a bit smaller.

With a car, and at that time of year, you'd be well advised to avoid the congested tourist areas in favor of the countryside. Killarney in particular can be a challenge to get in and out of when the tour buses are rolling, and places like Dingle, Galway, and Kinsale aren't much better.
Kenmare is a great suggestion. From there you'd be central for easy trips up to the National Park, the southern half of the ROK, and the very pretty Beara peninsula - a personal favorite.
Rather than Dingle or Killarney look at the stretch between Glenveigh and Castlemaine as a base of operations. From there it's a quick and easy drive along the northern half of the Ring, the scenic Skellig Ring Road that starts just west of Portmagee, the Gap of Dunloe and the Dingle peninsula.
Another favorite further up the west coast is the pretty market town of Clifden - located about an hour NW of Galway - from which you could explore Connemara at your leisure as well as nearby attractions like the Sky Road just west of the town and the short ferry ride from Cleggan over to the island of Inishbofin ... one of the country's best kept secrets.
Do try to include the meandering drive up the coast from Kilkee along the N67. It's one of Ireland's great scenic drives on a sunny day, and Kilkee itself is a cute little place for a lunch stop and/or a short hike along the nearby cliff walk, which is very nice indeed.

With 14 days you can easily split between two bases.

For the SW, then Killarney or Kenmare would work well. We actually preferred Kenmare to Killarney and found we could achievve everything from there just as easily.

uwe04 has given lots of good suggestions. I'd also add in Ring of Beara. Do go and find the Hag of Beara (weird and a bit scary) and also the short trip on the cable car to Dursey Island.

Then head head further north and base yourself in either County Galway or Donegal.

Somewhere around Galway City gives access to the Burren (wonderful limestone scenery and completely different to anywhere else in Ireland), day trip to the Aran Islands, Connemara with its wonderful scenery as well as the southern parts of County Mayo and Westport. There are ruined castles and abbeys to find too. The National Museum of Country Life near Castlebar is fascinating, especially the videos from the 1960s about life and customs in Ireland. Some of them are positively heathen!

Donegal again is scenically very good and does tend to be less busy than other parts of Ireland. I've always found Slieve League Cliffs to be much more impressive than Moher. There are small villages to find along with some great coastal scenery. There is also Glenveagh National Park too...

West: Galway (city) or Lisdoonvarna (town).

Southwest: Tralee or Killorglin, or further Southwest: Cahersiveen or Glenbeigh.