The refrigerator might not be the last place on earth to store potatoes, but it's pretty close. This is because potatoes don't fare well at temperatures below 45 degrees Fahrenheit (7 degrees Celsius). At that temperature, their inherent starches start to break down into sugars, which in turn can cause unfortunate changes to texture and taste, making the potatoes sweeter and tougher.
Instead, look for a dark, humid environment between 40 and 50 degrees Fahrenheit (4.4 and 10 degrees Celsius). If you live in a Northern climate you could store potatoes in a pantry, basement or a root cellar if you have one. If you live in a warmer part of the world, you can still store them in a cellar or kitchen cupboard — just make sure you use up your potatoes in a week or two. After that, the potatoes will start to sprout. Once you find the perfect storage spot, wrap the spuds up in a paper bag, rather than a stifling plastic bag, for storage.