I have at room temp:
potatoes
onions
garlic (all of above in special dark bags especially for keeping fresh at room temp)
whole un-trimmed leaks
and if i buy a melon or pineapple or similar large fruit i dont put it in the fridge when whole. (but do it cut or partly used)
also never fridge bananas.
i have a fruit bowl with various fruits in (at room temp obviously)
I get all my fruit and veg from the market each week, so things like spare apples / pears / satsumas and peaches / nectarines etc i keep in a brown bag on my fruit /veg trolley. (unless its very ripe then in fridge)
I keep berries / cherries in the fridge, and (if i remember) get out a few hours before eating so eat at room temp.
also any larger veg that dont fit in my fridge so easily (that im using within 3 days or so) go on the trolley
say swede / carrots / parsnips / cauliflower etc
If I go away for a few days then (if there is room) i move all fruit and veg from my bowl / veg trolley (except bananas) into the fridge (if theres space)