Nice cathedral and free entry
The Cathedral of Ciudad Real is one of the city's few notable attractions and is worth a quick visit if you happen to find yourself in Ciudad Real. This Gothic-Romanesque cathedral was built in the 15th century and its main nave ("hall" in cathedral-speak) is the second largest in all of Spain.
It was basically ransacked during the Spanish Civil War so it lacks many of the museum-worthy artifacts found in many other European cathedrals. It does, however, have a pretty stunning altarpiece from the Baroque period created by Giraldo de Merlo.
One quick note: this is more of an active church than a tourist attraction, so when you visit there will likely be many people reflecting, praying, and confessing.