If you are going to spend a week in Ireland, you may want to consider doing what I did my first time there, going around the entire island.
Enjoy Dublin by all means, whether it be the bars, nightlife, even a visit to Croke Park to catch a game of Hurling and they have a museum and tour. You must of course go to both the St. James Gate brewery/Guinness Storehouse, along with a tour of the Jameson Distillery.
I stayed in the Sandymount Hotel which is just a few blocks from the DART train. The food there was great, especially the breakfast they provide. Also visit e Roly's Bistro which is a few blocks away for some fine dining.
From Dublin I went south to Waterford (stopping along the way at various towns/pubs to interact with the locals)and took the tour at their crystal factory. We stayed at the Fitzwilton Hotel which was very nice.
Then I went out of my way further south to Kinsale on a recommendation, and thoroughly enjoyed it. A quaint little seaside town with good dining and wonderful people. As a matter of fact, since I didn't have reservations to stay there, a stranger approached me saying he noticed I was looking for a place to stay and the B&B I was about to go into was booked. He gave me several suggestions of places, and went so far as to offer to let me and my family stay at his house for the night if those places were also booked. [Who does that this day and age for a total stranger, me being from America no less. Plus I am 6'7" 240lbs, so had I been a loon, he could have endangered his family]
So I went to the Cloysters B&B he recommended, but they were full. So I wound up at the Friars Lodge which was nice, and it had WiFi and other modern amenities. Do make sure to drop in the Tap Tavern for some local flair, and The Spaniard was nice as well (though no Harp on tap). Do eat at Man Friday for a wonderful dinner.
Next I went to Lahinch hoping to get some surfing in, but that day the sea was as they say colloquially, like a mill pond.
So I ate at a small pub called The Corner Store which was very nice and open late, and stayed at the Lahinch Golf & Leisure Hotel which was also very modern and nice.
Then I made a stop in a town called Doolin to see the Cave & Stalactite billed as the 3rd largest in the world.
I am running out of time, but a quick rundown on the rest of my trip included seeing the Cliffs of Moher, Blarney Castle to kiss the stone, and eventually I made it up to NI and went to the Giants Causeway which was spectacular. When in Belfast I took the "Black Cab Tour" through a company called Belfast Attractions, and the driver brings you to the various troubled areas of NI, and you see former prisons, murals, etc. You can request to either get an Irish Nationalist or British Unionist driver, and both are typically former paramilitary people (IRA/UDA) who are now on the right path. They apparently have allowances to enter into the opposite sections of town, where as most former paramilitary people must stay in their own sections or be attacked.
Anyway, it is fascinating to see things like the "peace walls" and such. A visit to Stormont should also be in order if you have the time/interest.
I stayed at the La Mon Hotel & Country Club because it had a tennis court which few places in the RoI or NI do. It's bar has not only Harp on draft, but Harp Ice with it's distinctive stem covered in actual ice.
It is a little outside of the city of Belfast, but not far. We did the Titanic tour at it was interesting. Probably my favorite thing in Belfast itself (outside of it's historical aspect) was that most every bar had Harp on tap. You'd expect the RoI to have it being brewed there, but the people of NI apparently have better taste in beer rather than Bud Light and Heineken you see everywhere in the RoI.
Hopes this helps.
`