Given that you're in Dublin, it's worth also looking at the Dublin GAA website for the Dublin County. http://www.dublingaa.ie/
I can see there is a Dublin vs Galway fixture on May 28th which is 'SHC' the Senior Hurling Championship - it's the elite competition each year. I don't see anything for the following week in Dublin.
I've also looked at the GAA Master Fixture List for 2017 Master Fixture List
but there doesn't seem to be much on that week. See P6 on the schedule (Bealtaine is May, Meitheamh is June)
There is an Under 17 tournament on Wednesday May 31st but I don't know where the matches are being held. I've called the contact in the GAA and asked her to email me. If she gets back I'll post it here. http://www.gaa.ie/celticchallenge/
For GAA I'd also recommend visiting Croke Park which is the GAA headquarters and the stadium where the finals are held each year. They have a very good museum covering the history of the games and the organisation https://crokepark.ie/
Also if you want to get stuck in and try some Gaelic Games you could try 'Experience Gaelic Games' while in Dublin. It's a fun day to try it all out. http://www.experiencegaelicgames.com/who-is-it-for/
All the best,
Quick update. I got email back from Caoimhe in the GAA about the 'Celtic Challenge' tournament:
In relation to the Celtic Challenge the following fixtures may be suitable for your client on the 31st May:
Unfortunately, we have no games scheduled for Dublin on that date. All games commence at 7.30pm.