Store your tomatoes at room temperature, out of direct sunlight. An aerated basked it ideal. Please don't refrigerate your tomatoes. According to the Penn State Agricultural Magazine, A tomato will lose its aroma and flavor after just 40 minutes in the refrigerator. If you've sliced open a tomato and find yourself with a piece that you won't use in the next few hours, you can refrigerate this portion. I find the best way to store these left over pieces is cut-side-down in a small bowl. But, use it quickly before it gets mushy and looses all its flavor.