1) Go for a walk in the Triana neighborhood. Eat several meals in Triana.
2) walk through the Barrio de Santa Cruz. Shop, eat and go back there as much as you can.
3) visit the torre de oro museum
4) walk to the Los Remedios neighborhood and go to the park on a sunday afternoon. (I forget it's name, but it is high action.)
5) Visit Parque de Maria Luisa and Plaza de España. Rent a row boat.
6) take a cruise on the river. It doesn't cost much and what a view of the city!
7) tour the Isla de Cartuja: site of 1992 world's fair, former monastary, former ceramic factory.