One stuff comon to Northern Ireland and Eire is drinking. It's not only a reputation, Irish drink a lot ! So if you like good beer, good cidre or good whiskey you will enjoy your trip in Ireland. Of course the main beer in Ireland is Guinness but cidre is very well down especially from young people. Whiskey is very famous too but stronger and expensive. You can find good museum about whiskey in northen Ireland in Bushmills (near Giant' Causeway)

Ireland is not famous for his food... Indeed it's very difficult to find a good restaurant ! (however you can find lot of fast food...).
Irish breakfast is very famous but for some european it will be difficult to eat salt food the morning. However try it, it's not so disgusting ! (saucage, eggs, pudding...).

Tradition is very important in Ireland. There are lot of festival everywhere especially during summer. Major festival takes place in Dublin, Cork, Galway and Limerick. Saint Patrick's Day (14 March) is celebrated in every city and village in Ireland with lot of parade (Parade in Dublin is wonderfull...).
some festival...