On a budget, Newgrange & Brú na Bóinne still earns its price.
~€18 incl. shuttle; tours higher
Standing inside a chamber built before the Pyramids, with its famous winter-solstice light box, is a genuinely awe-inspiring brush with deep prehistory. The honest catch: access is only via timed shuttle from the visitor centre with no guarantee of a same-day place, it's about an hour north of Dublin, and you can't visit the monument independently.