I used the site Viator.com for planning my trip outside of dublin. They have a nice rail tours that last the day. You can easly plan your trip online. They Tour Guides are awesome as well!
The first time i went to Dublin i went during a busy weekend and had to stay at a hostle. I suggest u book now, cause even the best hostle were booked! I stayed at Avalon house, it was very lovely. near temple bar and a small grocery store so u can get ur own food instead of over paying in temple bar or for fast food. I suggest u just stay in the city for the weekend. Go around and see Christ Church, Guinness factory, walk around grafton and oconnell streets. For excellent night entertainment go to the Arlington, right near oconnell bridge, they have irish dancing every night, and its free to get in. I just got back from dublin 4 days ago for the 3rd time i absolutly love it there!
I agree with everything londonllama said. I spent 3 days in Rome alone and I felt like I was rushing around. I did pretty much what london recommends.
I would say London as well. Theres so much to do there, and you can also visit sites like Viator.com and take day tours to other places from London. Ive taken the Bath, Stonehedge tour and recommend it!
Ive been to Ireland a dozen times and the best tour I have ever taken was by this company http://www.overthetoptours.com/
I took the celtic experience tour and it was just the most amazing thing ever!
I think its the american standard to do the Blarney castle tour. Cliffs of Moher are beautiful and worth it if you can get over on that side of the country.
In Dublin Kilmainham Gaol is a a great site and gives you some good history of dublin. Have a Guinness at the Arlington and see the show one night. Stay away from temple bar unless you want to meet up with the rest of the Americans! You could stay in dublin your whole stay and just take day tours out. I usually use Viator.com for my day tours. Hope it helps!