I think that by trying to cram so much into 9 days, you are going to miss the essence of Ireland. You are doing in 9 days, pretty much what I have done in two 18 day trips. I would either go north or south of Shannon, and loop around through Dublin and end up back in Shannon. If you are going soon, I would go north and spend some time up in Donnegal and avoid the crowds that the Southwest sometimes has.

As for attractions, being a kid at heart. Giants Causeway is really cool. The Cliffs of Moher are cool, but not as cool as Slieve League (sp) in Donnegal. There are a lot of fun kid things to do in both Dublin and Belfast.

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