The idea of a private island is one of the most seductive in travel, especially when the microdot is located in some obscure and far-flung archipelago, thereby confirming that the world is still much bigger and more exotic than is sometimes assumed. Here at Andrew Harper, traveling halfway around the world to review a remote atoll taxes our ingenuity and resources, but we keep a list of likely candidates and over time they find a way onto our itineraries. Here are five that we are most anxious to visit.