Are you going by air or ferry? All above suggestions are ace, however if starting from Dublin it will eat into your time getting over and back to the West.
Knock International or Shannon airport are good starting points. You're ready to rock from either!
Shannon for Clare, Cliffs of Moher (sunsets), beaches at all along from Kilkee to Lahinch. Moher not too far from Lahinch. Or North Kerry on the river Shannon ferry from Killimor to Tarbert where there are great beaches at Ballybunion, Banna, Carrahane etc.
If you can get a flight to Knock, then it's Westport, Newport, Mulranny and Achill. Or the other direction, Murrisk (Croagh Patrick), Louisburgh, Killary Harbour, Silver Strand and so on. Galway if you can get that far down.
Absolutely glorious part of the world. I hope you enjoy it a lot.