How long do you want to store them? I'm thinking tomatoes are fine when left at room temperature, but maybe for only a day or two. You could make a nice salad of olives, oil, tomatoes, salt pepper and vinegar. Celery is going to have the leaves go limp but the stalks might still be OK - for a couple of days. Onions for sure are OK without refrigeration. Carrots are OK without refrigeration, I think.
I have read that apples can be kept at room temperature for a few days. I buy apples from a discount bin at the supermarket and make smoothies from them. They stay at room temperature for about a week in my experience, with some spots of decay. However, they were less than beautiful pieces of fruit to begin with. Old apples and very ripe bananas make one of my favorite smoothies!