June is the start of the summer in Ireland providing 17 hours of daylight (sunrise at 5 am and sunset at 10 pm). Galway's weather is amazingly unpredictable. The climate is particularly temperate, with little difference between highs and lows throughout the year. June is mild, with averages just below the 20° Cs (high 60° Fs). The location of County Galway, situated on the west coast of Ireland, allows it to be directly influenced by the Gulf Stream. Rainfall occurs in every month of the year. You are  advised to take rain gear or an umbrella with you.
For more information and the current temperature check http://www.meteireann.ie/