The main shrine in Kagoshima City is Terukuni Shrine, marked with a huge torii.
Perhaps its most distinguishing feature is the tree in front pruned into the shape of a bird with outstretched wings. It is not an ancient shrine, being founded in 1863 and enshrining the daimyo of Satsuma, Shimazu Nariakira who ruled for 7 years until his death in 1858.
Like many of the modern shrines that worship rulers, politicians, generals etc I find it quite a sterile place. I personally can find nothing in his story that would make him an object of worship for me, but then I find authority based on violence and or wealth an unpleasant and disagreeable concept. He was one of the daimyo that supported the overthrow of the government and a return to Imperial rule, so it was an imperial decree that enshrined him as Teruluni Daimyojin
There is a museum in the shrine that does have a good collection of historical artifacts connected to the Shimazu rule though.