Will avocado stay fresh longer if stored in the refrigerator?
Ripening of the avocado is slowed down greatly by refrigeration, so it is usually a good idea to let the avocado ripen fully at room temperature. Once it is ripe, it can be stored in the refrigerator for at least a week. This way, it is ready to use whenever you want it. Fortunately, there is a day or two when the avocado is ripe, but not too ripe, so if you check on it everyday when ripening, you will be able to save it at the correct ripeness without worrying about it too much.

Putting an unripened avocado in the refrigerator may prevent it from ever ripening completely. Once cooled to near freezing (40F in most refrigerators), it seems that some avocados (maybe it depends on the type) don't ripen anymore, even when removed to room temperature.