Great choice on a holiday destination.
The south, south west and west of Ireland are the most scenic locations, as well as having kept the tradition of old Ireland.
Starting in Cork, stop off in Kinsale, check out Cobh, the last stop of the Titanic,
Glengariff, Bantry, the ring of Kerry, avoid Limerick, Clare is beautiful, Galway, the Aran Islands and on up to Donegal.
Avoid fancy restaurants and chains and check out the smaller diners in non tourist towns. Country pubs are also more fun and can also be cheaper.
The Spaniard in Kinsale is a must.
PM me your email and I'll do up a google map with stuff worth seeing and cheap places to stay.