I have a conference in Limerick coming up in July, followed by two and a half days of free time until my afternoon flight out of Dublin. Where should I go and what should I see?

Background: I haven't been to Ireland in 15 years and don't really remember anything except that it was green and it rains a lot, so the country is pretty much a blank slate to me. My primary interests would probably be nature or Celtic sites, as I'm not particularly keen on whisky or Guinness. Ring of Kerry or the Dingle Peninsula, perhaps? The final caveats are that I'll be limited to public transport (yes, I know Ireland's great driving country, but I don't have a driver's license), and I'll be on a fairly conservative budget, as I don't see the point in splurging on hotels or meals when traveling alone.

Any advice would be much appreciated ^