Hello!
Our family of four is traveling from Schull, Cork to Ring of Beara and staying in Kenmare. After that, we have two nights left and want to do Killarney National park as well as the Cliffs of Moher and leave from Shannon on the third day. Is there a town we can stay in both nights that we can reach after Killarney National Park - visit Cliffs of Moher the next day - stay again and head to Shannon? Thanks for any advice/tips!

Ennis is an option. If you just want a place to stay, look at the Courtyard B&B next to Bunratty Castle. Not much near there but it's easy to get to, inexpensive, and very comfortable.