Seville is the capital of the province of Andalusia and you'll be most aware of this at the iconic Plaza de España. Once you've regained your breath from the beauty, take a boat ride, listen to the street musicians and applaud the flamenco dancers. The mosaics depicting the different cities in Spain are definitely worth seeing. It will take you a while to get around them.
Plaza de España is adjacent to the beautiful park where the Moorish Pavilion stands. If you like Moorish architecture, be sure to stop by.
If you want to see the cathedral, or see it from the top of the tower (which is truly magnificent), buy your tickets in advance online. It gets crowded in high season and you really don't want to stand in that line.
Not far from the cathedral is the royal castle, a little preparation for a visit to the Alhambra.