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It's either fly all of the way or fly to a major city like Chicago or New York and drive the rest of the way. There is no passenger train service in South Dakota and bus service is pretty bad, in more ways that one.
Thanks for all your replies, I was just checking with hope that there was somewhere near we could travel to and maybe get train on to Sioux Falls. It's such a long journey from Dublin and expensive,nothing I can do about that. Many thanks.