No one is quite sure if Kinmeng Island is part of China or Taiwan. For what it's worth, Chiang Kai-shek, left a calligraphy inscription on this island, urging his troops to fight on and to "re-take the Mainland from the Communist bandits".
You won't find any bandits here, just a charmingly small town of Kincheng. You can easily walk around and check out various museums and monuments to the war, the cultural villages, and buy a "wind lion god" statue. It has a couple nice vegetarian restaurants and one random Irish pub.
There are regular ferries from Xiamen. Boats are 160 RMB (130 plus 30 tax) from Xiamen to Shuitou and run once an hour between 0830 and 1730 both ways. Departure in Xiamen is from the International ferry terminal at Dongdu Road (东渡路), the same complex as Xiamen International Cruise Center (厦门国际邮轮中心), just north of Bay Park.