You can find out about the history of Piura with a trip to Armas Plaza. While in the area, you can find time to visit its shops.
Take a campus tour or just explore the area of National Universtiy of Piura, during your trip to Castilla. While in the area, you can find time to visit its shops.
Though Hospital Regional José Cayetano Heredia might be what brings you to town, perhaps you'll have a chance to explore more of Castilla while you are here.