Bananas
They retain better nutrients when the bananas are not in the refrigerator. Cold temperatures will only slow the ripening process. Furthermore, the darkness and the humidity of the fridge only rot the fruit. On the kitchen counter is the best place to keep them.
Basil
Remember, your basil doesn’t belong to the refrigerator! Place the herb instead of a cup of fresh water. Blanch it first and freeze it if you intend to store basil for a long time. Odd, but it works.