As you'll be doing your sightseeing in the city centre (about 10 minutes by bus or 20-30 minutes depending on how quickly you walk), I'd recommend you do most of your dining there. I'd describe most of the food in the better restaurants in Dublin as French/Irish. Most are located in D2 (south city centre) with the odd one or two in D1 (north city centre). Dublin city centre is separated by the River Liffey, so it's fairly easy to get your bearings.
The Exchequer - Gastropub. You can reserve a table or just show up and eat at the bar.
Queen of Tarts - Tiny original branch opposite Dublin Castle or newer and bigger branch on Cow Lane about 50 metres away. For lunch or afternoon tea. Cakes and pastries are fab.
Chez Max - French cafe at gates to Dublin Castle.
Silk Road Cafe - Located in Chester Beatty Library (more of which later) behind Dublin Castle. North African, Eastern Mediterranean and Middle Eastern food.
Green 19 - Wexford Street/Camden Street area is the happening part of Dublin at the moment. Mains are all €10. Comfort food. The champagne lemonade (non-alcoholic) is delicious.
The Winding Stair - Just over the Halfpenny Bridge in D1 in what used to be a bohemian bookshop/cafe. There's still a bookshop downstairs. Try to get a seat by the window for some quintessentially Dublin views.
La Maison - French bistro behind Powerscourt Townhouse shopping centre
L'Gueuleton - French again. They don't take reservations, but I've never had to wait.
101 Talbot - One of my favourites. It's quite lively and generally frequented by theatregoers attending plays at either the Abbey or the Gate. Casual, but great food.
Thornton's - One Michelin star. Lunch is incredibly good value. Best to reserve ahead. Just don't ask for chips.
Chapter One - One Michelin star. Next to the Dublin Writers Museum on Parnell Square in D1 hence the name.
Pearl Brasserie - Across the road from Government buildings. French/Irish.
Patrick Guilbaud - Two Michelin stars. Next door to Pearl. Expensive and possibly the only restaurant in Ireland that could be described as somewhat stuffy. Incredible food though.
OK, that's the restaurants out of the way. Next is pubs and bars. Where do I even begin?
The Brazen Head - Ireland's oldest pub. Near Christchurch
The Church - In D1 in a, yes you've guessed it, deconsecrated church.
The Library Bar - Inside the Central Hotel on Exchequer Street. Always reminds me of Blake Carrington's study from Dynasty.
The Dawson Lounge - Probably the smallest pub in Ireland, but plenty of character. Not for the claustrophobic though.
Cafe En Seine - Near the Dawson Lounge, but worlds apart in atmosphere and size.
The Long Hall - Victorian era pub. One of the best pints of Guinness in Dublin.
The Market Bar - A converted sausage factory. They also do tapas.
Just across the road from the Market Bar and above L'Gueuleton, there's a bar with no name that's frequently referred to as the Secret

bar.
That's just scratched the surface as far as pubs and bars go, so hopefully they'll be something there that you fancy.
Sightseeing in Dublin:
Guinness Storehouse - I suppose if you come to Dublin, it has to be done. Booking online gives you a 10% discount on the (expensive) admission and you don't need to queue for your ticket. You can just pick it up at the information desk. Entry includes one drink (Guinness or otherwise) at the Gravity bar
Trinity College - Ireland's oldest university and home to the
Page Book of Kells. The Old Library is worth the price of admission alone. Small discount for booking online.
Student guided tours over the summer months are apparently quite good, although I've never been on one.
Christchurch Cathedral - Ye olde ancient church.
St. Patrick's Cathedral - Ye another olde ancient church.
Dublin Castle - Seat of British rule when Ireland was still a colony of the UK. Mr. allezfred and our friend did the guided tour and thought it was fantastic. Quite popular so show up early.
Chester Beatty Library - One of the largest collections of Oriental and Islamic art in Europe. European Museum of the Year 2002.
The National Museum - There are actually three separate museums within Dublin that come under the banner of the National Museum. The National Museum on Kildare Street (next to Leinster House, the Irish Houses of Parliament) displays archaelogical artifacts (mainly Celtic and early Christian). The Natural History Museum on Merrion Square has recently reopened (it was closed a few years ago when a marble staircase collapsed

). It's frequently referred to as "The Dead Zoo". Further away and across the river from Guinness is Collins Barracks which is the Decorative Arts and History branch of the museum. Admission to all the museums is free.
National Gallery - Lots of paintings.
The Hugh Lane - The modern contemporary Irish art can be ho-hum, but the reconstruction of Francis Bacon's studio is fascinating. Admission free.
Dublin Writers Museum - Next to the Hugh Lane. No shortage of material for display.
Besides the above places, I'd recommend just walking around Grafton Street, St. Stephen's Green, check out the Georgian Houses around Fitzwilliam Square.
Other tips:
Butlers Chocolate Cafe - Several branches in Dublin and around Ireland (there's even shops in Karachi and New Jersey

). With your coffee, tea or whatever you get to choose a chocolate truffle or praline.
Penneys - Irish retailers do affordable fashion really well and this is the king of them all. The mens selection can be a bit meh, but the womens and childrens are bang on trend and inexpensive.
Carrolls - For cheap and tacky souvenirs!
Avoca - On Suffolk Street in D2. Cute and stylish clothes, home furnishings and food. Deli downstairs and restaurant on top floor.
Kilkenny Design - On Nassau Street in D2. Full range of top quality Irish souvenirs.
While there are places worth visiting, in general I would give Temple Bar(f) a wide berth unless you want to spend your whole time in Dublin with other tourists eating overpriced, substandard food and dodging hen and stag parties.