For a long time I have been looking at pictures of and researching the town of Écija and have it on my wish list for the future. It is about 85 kilometers from Sevilla, heading towards Córdoba. No train station but by bus it is a little over an hour. It's nickname is the city of towers and it has its fair share of towers, churches, and beautiful Casas Palacios. You can follow the Ruta de los Palacios and visit many of these beautiful, elegant old structures, some very Moorish. The town has a great tourism website. Look up Turismoecija.com. This is not a place on the American tourist radar but is exactly the smaller town, less crowded hidden gem destinations that I very much appreciate.
You must go to Córdoba. It is a jewel. I liked Jerez - spent Christmas there one year. Like Acraven said in her reply, I also think Mérida is too far for a daytrip, especially using public transportation - and I also agree with her that the Roman ruins and museum are the attraction there, not the town itself.