There is a route called 'the wild atlantic way' which travels up the west coast, would be one option.
Galway would be my destination of choice. Fly into dublin and get one of the direct buses that go from Dublin airport to galway city. Galway city is very small and you can walk the length of it in about 5 minutes, great city for pubs and live music. It's also a hub for tourism on the west coast, you can take day tours, which are excellent in good weather, to aran islands/cliffs of moher/connemara. All your buses are pretty small and include a lot of stuff and they all leave from the same bus station that you will arrive into from dublin airport.
If you came in the summer with good weather I would stay on the aran islands for a night or two, serious session.
From Galway you could then head to kerry, The ring of Kerry is really nice.
Don't waste time in dublin, it's just like any other city, boring .