The best way to travel Ireland is to rent a car. The trains link major cities and towns in the middle and the buses cover more places but are limited in terms of times.
Ireland is quite small and it can be difficult for the best things to stay hidden. For example there is a lesser know but quite important stone circle in Kenmare (but no match for samples on The Burren), a good example of a 'Cromwell' bridge and a pretty good religious site. Near Sligo there are quite a few passage tombs/cairns/burial mounds - Carrowkeel near Castle Baldwin for example and there are others in the same area such as Carrowmore(check this - http://www.carrowkeel.com/) - but they are hardly world beaters (as opposed to say Newgrange) or have the accessibility and that is why they are less visited and less interesting. The friar's abbey at Claregalway is a great ruin (certainly better than the preserved sanitised church ruins at Boyle) but, apart from its size, it is identical to a million other church/castle ruins through out Ireland such as those at Gurcheen, Jarlaith's in Tuam (or Tuams' high cross, or Tuam's water mill, or the site in Tuam where the last executions of the civil war took place) or even Finnstown Abbey/Esker Church ruins in Lucan (which has a nice Cromwell style bridge nearby - get the 25A/B bus from Aston Quay). And that's the way of most things - they are popular and well known because, for some reason, they are the best as opposed to those I have listed which are not the best examples of such.