I prefer room temperature fruit but I'm not sure about how long it will keep outside the fridge. Apples and peaches are obviously fine but what about something more perishable like strawberries?
Definitely refrigerate the strawberries. Berries in general, once picked, are short-lived and should be refrigerated (if not eaten) as soon as possible, especially in hot weather.
Stone fruits such as peaches, apricots, nectarines should be kept at room temperature until ripe, then may be refrigerated until ready to eat. Ditto that for pears.
Citrus fruits do well in the refrigerator. And of course, bananas go unappetizingly brown (though still edible) in the refrigerator, so it's best not to put them in there unless they are going seriously overripe and you are not ready to eat them. (At that point, I generally peel and freeze them, cut in half or smaller--great base for smoothies.)
re: LT from LF
Re strawberries, I have been having much better results since I started following advice from Joy of Cooking (and other sources), echoed by other posters here: Remove the strawberries from their original container, eat (or toss) any berries that are overripe, damaged, or exuding juice, and refrigerate the rest, UNWASHED. Don't wash them until it's time to use them, and then only as lightly as possible.
Until recently, I had always followed my mother's practice of washing the berries as soon as we got them home from the store, drying them, and then storing them in the frig in a bowl with extra paper to absorb excess moisture, The new procedure seems to keep them fresh and juicy (and better-tasting) longer.
Though I refrigerate certain fruits (like berries) for longevity, I too prefer the taste/texture/juiciness at room temperature. So, if I know I'm going to want strawberries after dinner, I take out a portion beforehand so that I can enjoy them at their best.