Kashima Castle Ruins are a modest but pleasant park near the centre of town. The castle never had the grand silhouette of Japan's famous keeps, and much of it was lost in the Saga War, but surviving gates, moat remains, and seasonal lilies make it a good quiet counterpoint to Yutoku Inari.
It is worth a short stop if you are already walking through town, especially before or after the Hizen-Kashima station area.