OP don't be put off by all the posters saying avoid Dublin. I think if you've never been to Ireland & have a desire to do it then by all means do so!
Depending on how long you plan to stay you could stay 2 nights in Dublin & then get the train to Cork or Galway for 2 nights. You could fly into Dublin & fly home from Cork etc.
As for Dublin, again depending on your interests really- there's loads to see & do!
I woul d recommend staying on the southside in the main city centre. Have a look at Brooks Hotel or on booking.com to check out prices.
If you like literature / history there's loads to do for sure!
I recommend The Tenanment Museum on Henrietta St, a once beautiful but still interesting Georgian St. The Little Museum of Dublin on St Stephen's Green is fun & another opportunity to have look inside a beautiful Georgian house..
Epic Museum is an award winning museum looking at emigration
Trinity college is worth a wander & The Long Room library & Book of Kells is fab but book tickets online to avoid queues
For a quirky history experience vist St Michan's Church where you can visit the crypt & see Bram Stoker's resting place
Have a coffee in the historical Bewley's Coffee House & lunch in Davy Byrne's famous literary pub where writers such as James Joyce, Brendan Behan & Patrick Kavanagh hung out.
Book a ticket to see a play in the Olympia Gate or Abbey theatres.
Have a drink in victorian pubs such as The Long Hall, the Stags Head or Neary's
See art & have lunch in The National gallery or the Hugh Lane gallery or The RHA Gallery.
Have a stroll over the ha'penny bridge, through Merchants Arch, up Grafton St, into the Stephen's Green, down Baggot St
Or visit the James Joyce Centre on North Great George's Street & follow one of their walking tours through what's left of Joyce's Dublin.
Visit Dublin Castle & the Chester Beatty museum in there then get fish & chips from traditional chipper Leo Burdocks.
Visit Christchurch & St Patrick's Cathedral & the Irish Museum of Modern Art & the Guiness Factory - all in the same general area
If you'd like similar tips for Cork or Galway just let me know