Apart from the odd glass of Jameson's at corner Irish bars which don't look like they could make a passable cocktail, I've managed to ignore Irish whiskey pretty successfully for most of my drinking life.
If you're looking for something a little more unusual than green beer to imbibe on St. Patty's day, try The Good Cork Cocktail. The recipe comes from bartender Philip Ward of Mayahuel in New York City.
Strong black coffee, whiskey and one level teaspoon of brown sugar stirred into the coffee. Pour the aged heavy cream over the back of a spoon held over the glass... then you drink the coffee through the cream. Heavenly.