I went to the farmers market this morning and picked up a bunch of stuff that I won't have the opportunity to use until the end of the week. What's the best way to store: carrots, scallions, fennel, eggplant, and already very ripe tomatoes?
Put the scallions in a glass of water in the refrigerator. Would be a shame to chill those tomatoes, but if you have too...
Carrots keep fine in the crisper drawer. Store eggplants room temperature away from direct sunlight.
I would wrap the fennel and carrots in a paper towel and dampen it with a few sprinkles of water from the tap. Then put it in a plastic bag, and stick in the vegetable crisper. This is my go-to trick with lettuce, asparagus, and a lot of other vegetables; it goes a long way to helping them hold their texture and quality.
Depending on how you plan to use the tomatoes, you can always freeze them whole, which makes it easy to remove their skin once thawed. I've done that when in a similar situation.