When you're in Elche, we recommend also a short trip to nearby Alicante. Not just because it's a beautiful coastal city, but to visit the Estadio José Rico Perez of Hercules Alicante. The once so proud club has fallen deeply and gotten in financial trouple, but the stadium is still wonderful. The 1982 World Cup was played here as well, including Argentina with a young Diego Maradona. The floodlights are awesome and the stadium is charmingly asymmetric.
A little west of Elche you'll find a nice little stadium as well: the Estadio Municipal Enrique Miralles in Crevillent, home of Crevillente Deportivo.