If you want to see the Sevilla that is fairly free from the influence of tourism, step across the Triana Bridge to Triana and you'll see it. The riverfront street, Calle Bettis offers great views across the Guadalquivir to Sevilla and you'll also find some authentic restaurants and shops.
The main church of Triana is Santa Ana. I love the brightly colored exterior and the tower can be seen from across the river as you'll notice in my previous tip. It's located on Correa.