Have a great trip in June.
I live in Dublin. The luke's post about pubs on every corner in the city is very accurate. There are plenty of crappy tourist trap one like in any city. I recommend O' Donohues on Baggot st near St Stephens' green. Anyone will tell you where it is. Most evenings there will be local/amateur musicians playing good traditional music. It can get cramped in there but it is one of my favourite Dublin pubs. If the weather is nice St stephen's green is a nice place to walk through and have an ice cream. Dublin is pretty expensive. Pints of beer around 5euro in most city centre places although GUINNESS is a bit cheaper.
A real local tip here, outside of the 5 star hotels the best place for a traditional Irish fried breakfast is a small coffee shop called "Gerries" on a tiny side street called Montague st, again near St Stephen's green. It's not exacly gourmet but full of good bacon, sausage and grease!
Enjoy your holiday. PM nearer june and if I have time i'll give you as much details about good spots to check out. Someone on the thread already suggested Giants causeway in the north. Yuo should definately go there either by train or better if you hire a car.
The Doc