No need to refrigerate. Romaine Lettuce seems to last much longer if you separate the individual leaves from the head, shake off the excess water, let them air dry or pat with a paper towel, and store them loosely in a sealed plastic bag or flat plastic container. Once again, leaving a paper towel in the bag will help. You won't be wasting any of this celery. Any odd size pieces or excess celery can just be put in a zip-lock and used first.
Cabbage lasts many, many days un-refrigerated.
Don't wash it and leave the original outer leaves attached. Stow it away again un-refrigerated and go thru the same process the next time. Try not to cut into the head until you plan to use it all. Sun Dried Tomatoes last almost forever if you store them in a jar filled with olive oil. Listed here are many of the items I'd try to keep on board for my own eating enjoyment.