The fruit bowl on the dining table always has apples, oranges and grapes. They don't last very long as we tend to graze on them, after meals, so no problem of spoiling. Bananas are kept on a spike next to the kitchen fruit thingy, which holds things like kiwis, lychees (mine - all mine!) and passion fruits.
I do keep eggs in the fridge, though I know it's better not to, and tomatoes too because if the weather is warm they very soon go "off". I store potatoes in a cupboard but carrots and greens go in the "salad crispers" in the fridge. Avocados also live in the fridge because they go off fast and strawberries and other soft fruits go in there for a maximum of 2 days. If we haven't eaten them by then they're manky.
Cheese - definitely in the fridge but in an airtight box. Jam and fungus - I've been scraping it off for years, not that we get it that often, but I don't tell Nik as she wouldn't eat it if I did.
