Fanning Island - As of the time of my visit there in 2002, there was no electricity on this island.  Take the tour for a few bucks American.  Go to the jungle - though the tourists will go to the beach.  There is a small church in the jungle with a metal roof.  On Christmas day in 2002, a fingerless man played Christmas songs on a battery-powered keyboard to the delight of the congregation (of men, women had to wait on the outside of the perimeter of the church while they cooked food over campfires).  Very cool!