Hi, you have a choice of 4 live top quality rugby matches on Fri 24th or Sat 25th March depending on where you are in the country at that time. If you are in Dublin on the 24th, Leinster play at 19.35 in their home ground, RDS, in Ballsbridge. For a better experience I would recommend you go to either the Connacht match at 15.15 on the Sat in Galway city or the Munster match at 17.15 in Limerick (known as the the home of Irish rugby). Other option is to see Ulster play in Belfast at 19.35 on the Sat night..
You will have no problem getting tickets for any of the matches by turning up on the day, no need to book in advance. That weekend is the 3rd last round of matches in the League (URC - www.unitedrugby.com) and all of the games, bar the Leinster game, will be crucial for the Irish sides to win, based on the current League standings. I am from Munster so would love you to visit Limerick (only 1 hr 15 drive from Galway) as the atmosphere in Thomond Park is unrivalled (IMHO) for a rugby game. Cost of tickets vary from €20 to €40 depending on whether you want to stand on the Terrace or sit in the Stand.
There are no National Hurling games on that weekend which I would have also advised you to attend but there are National Football League games on Sunday in Galway & Dublin - of the two games, the Galway one would be the more competitive as they play Kerry, who are the current All Ireland Football champions. Again tickets will be okay to buy on the day and cost €18 for a seat. Look at www.gaa.ie for all the details.
How about taking in the Munster rugby game in Limerick on the Saturday evening, staying the night and then drive up to Galway on the Sunday morning to get there for the Gaelic Football game starting at 13.45? Enjoy whatever you go for!