Unripe tomatoes are still green and should be stored stem side down in a cardboard box or brown paper bag. This will encourage ripening.
Ripe tomatoes should be kept stem side up, at room temperature and away from sunlight. Eat them within a few days for best taste.
Overripe tomatoes develop very red flesh and are soft to the touch. Refrigerate to get about 3 more days of freshness. Before eating refrigerated tomatoes, let them come to room temperature. This allows flavor to develop.