Generally
If tomatoes are underripe or just ripe, store them at room temperature on the counter, away from direct sunlight, to help them ripen fully or maintain their flavor. If they're overripe and you're not ready to use them right away, store them in the refrigerator to slow down spoilage. Let them come back to room temperature before eating for the best flavor.
Do not store with
Leafy greens, cucumbers and onions. Learn more about what not to store together.