Traveling through Ireland?

I am planning on flying into Dublin next May and I would like to travel West mostly. What is the easiest and/or cheapest way to travel through Ireland. Which cities should I hit? I've heard that Eurorail and other trains are expensive. Also, should I then make my way back to Dublin to fly back to the US or fly out of an airport in West Ireland? Thank you SO much!Traveling through Ireland?
I'd travel by bus - Bus Eireann travel all over the country and their fares are decent enough, certainly cheaper than rail prices. There are also private bus companies in different areas that can be even cheaper, or specialist backpacker services like Paddywagon Tours (not as cheesy as it sounds). I'd go from Dublin directly to Cork (with a stopover in Cashel) and work my way along the coast through Kinsale, West Cork, Kerry (the Ring of Kerry from Kenmare round to Killarney), a night in Limerick city, then Clare (Cliffs of Moher, the Burren %26amp; Poulnabron dolmen, Ailwee Caves, Ballyvaughen) and from there up to Galway city (good for music %26amp; night life) out to Clifden, Connemara, the Aran Islands, onto Mayo, Westport, maybe even Achill Island and finally over to Sligo and Yeats country. From there, it's six of one and half dozen of the other whether you go back to Dublin or down to Shannon to fly home. To do that itinerary properly, you'd need AT LEAST 2 weeks, better with 3. If time is more limited, go straight to Cork, from there to Kerry, up to Clare and Galway. If you can, work some festivals into your visit - see the last website below.