This article has excellent information on what to do with your homegrown (or farmer's market purchased) tomatoes, including whether to refrigerate, how to store on your counter, and more.
Tomato-storage guidelines:
- If at all possible, buy only as many perfectly ripe tomatoes as you can eat within a day or two, keep them stored stem side down on a flat surface at room temperature, and make sure to eat them all within the first day or two.
- If you buy underripe tomatoes, leave them out at room temperature until they're fully ripened, then move them to a cooler spot for longer storage.
- If you have a wine fridge or cool cellar, store all ripe tomatoes that you can't eat within the first day there.
- If you don't have a wine fridge or cool cellar, store all ripe tomatoes that you can't eat within the first day in the refrigerator.
- If you're storing tomatoes in the refrigerator, it may be better to locate them on a top shelf near the door, which is often warmer than the bottom and back of the fridge.
Credit: Serious Eats