I think Sel is right: I don't know of any air Carrier that flies direct from the U.S. to Sevilla. Once, we flew Iberia TransAtlantic and said Sevilla was our destination. We had to pass thru Immigration & Customs and change planes in Madrid, but it cost the same to Sevilla as to Madrid.
May 30 is Pentecost Sunday and the peak of the feria del Campo and Romeria al Santuario de la Virgen del Rocio just across the Donana in the Province of Huelva. So, maybe you want to go to Sevilla first and come up to Madrid for some of the San Isidro festivities.