The most important shrine in Kagoshima city is the Terukuni Shrine, easily found by the giant white torii in the downtown area.
As shrines go it is not very old, being founded in 1864. Terukuni Shrine was rebuilt after being damaged in the final battle of the Satsuma Rebellion, "Saigo's Last Stand", but the current structures date from the post World War II reconstruction following air raid damage.