Southeast or Southwest Ireland

What attracts you to Ireland? If it is the scenery, focus on the west side of the island. Starting with the southwest, consider Ring of Beara, the Gap of Dunloe, the Dingle peninsula, the Burren in County Clare, Connemarra and Inishmore (the largest Aran island) in County Galway. Of course you don't have time for all of these if you are only staying a week, but those are good areas to research. I assume you are renting a car?

IMHO Dublin is just one more large city and I would skip it unless you have Irish roots on which you are focusing. If you do decide to forgo Dublin, consider switching your plane tickets so you fly into Shannon. If you can't, two good stops near Dublin are New Grange north of the airport or Glendalough south of Dublin.

If I was choosing between southeast and southwest, it would be southwest, hands down. There is just so much more to see in that area. If you aren't tied to flying into and out of Dublin, you might think about flying into Dublin and out of Shannon so you don't have to spend time getting back to Dublin.

The Southwest is beautiful and there's a lot to do. I agree with the others and would add the Cliffs of Moher and in Galway, the Trad On The Prom.

Thanks for the suggestions. In all my other European travels I have just taken the train. Is that going to be a big problem in Ireland? I can't drive a stick so it will depend on who travels with me. Also, I am a little nervous about driving on the other side of the road :)

The train system is not very extensive in the west, but the bus goes everywhere. You can check schedules at www.buseireann.ie. You can also rent automatic cars, and I didn't find it tough to get used to.