I went to Croke Park last year. That stadium tour is one of the most moving tours I have taken in any country, anywhere. The Superdome is inextricably linked to New Orleans and its recent history given it was a shelter of last resort during Katrina, but Croke Park may well surpass it in terms of historical significance and the national identity. The part of the tour where the guide takes you through the events of Bloody Sunday where the Black & Tans entered the stadium and shot and killed players and spectators is absolutely gripping.
If I could travel back in time to any one sporting event, it might be the England/Ireland Six Nations match-up at Croke Park from 2007 (England's first appearance there in 80+ years).
Also, I'd wager that most GAA players are tougher than American kickers who could conceivably go through all of college football without anyone laying a finger on them.