As all people before had already told you, Dublin is a great city. In addition to all the recommendation I'd certainly advise to take the Music Pub Crawl starting at about 19.30 and lasting for about 3 hours in different pubs with stories and Irish songs. Don't miss this wonderful experience.

Also, you can visit within a day tour from Dublin the marvelous Antrim Coast with Giant's Causeway. You take the early morning train to Belfast and ask the company that the bus will wait for you at the railway staion. You can call to the tourist office of Belfast to ask the phone number of this company- that's what I did. You can also make at the end a stroll along the center of Belfast. Don't miss this tour if you can. I know that it's also possible to organize such a tour from Dublin, but for more money. The tour in Belfast costs about 20 pounds.

Another jump off can be to Killarney or Cork, though the former is much more recommended with its real Irish soul and great French Castle.

Sincerely, Alex Jerusalem Israel