More vegetable-storage tips:
Bananas should never be kept in the refrigerator, as they are sensitive to cold and go black.
Avocados should be stored at room-temperature until ripe, then transferred to the refrigerator unwrapped.
Citrus fruits - grapefruits and pomelo are cold sensitive, and so should be stored outside the refrigerator. Oranges and lemons, on the other hand, will wilt if stored at room temperature for too long, and so should ideally be stored in the lower shelf of the refrigerator.
Onions have a strong smell that can take over your entire refrigerator, so beware. I store them in the refrigerator in a plastic bag, because that way my eyes sting less when I chop onions (although I wear chemical laboratory protective glasses, too).
Watermelon - a ripe watermelon can be stored in a refrigerator for about a week.
Sweet potato - should only be stored at room temperature; develops a queer taste and cold damage if refrigerated.
Garlic - cold storage is best, because otherwise it will sprout. In the refrigerator it can keep for several months if the air circulation is good. I sometimes let my garlic sprout on purpose and use its leaves in salads, the same way as green onion.