I agree with Peter about the Flamenco show. Our hotel booked it for us. Even though it was just around the corner from our hotel, we got lost on the way there! Part of the fun in Seville is getting lost in Barrio Santa Cruz. I loved walking around the "Kissing Lanes."
Another thing we really enjoyed was a carriage ride through the city. Picked up near the cathedral, we rode through the city, Parque de María Luisa
(which, to me is a hidden treasure), and on to Plaza de España
I wrote an article about Seville at SushiandGelato.com
The article is about things to do with kids, but really, the items are just as fun for adults.
Seville was a highlight of our Spain trip. You'll have a great trip!