How to store cake
Don't know how gooey or dairy your sour cherry bars are.
If very, probably refrigerate at once (as with cheesecake, whipped creanvor buttercream frosted cakes).
Otherwise; guideline is 1-2 days at room temp, about a week in fridge, or 1-2 months frozen
I never store cake in the refrigerator. I either keep it on the counter for a couple days or freeze it for a couple weeks. After dairy and eggs are baked (provided they're baked properly) they are entirely safe at room temperature.
Why no refrigeration?
Baked goods (especially cake and bread) stale about 6 times faster at refrigeration temperatures, so unless there are perishable components (custards, curds, creams) I don't refrigerate. Another reason is, for baked goods with butter as its main fat component, chilling them will change the texture because the butter is in its solid phase. It makes the baked good taste dry in the mouth, so if you do refrigerate butter-rich pastries and cakes, always bring them back to room temperature before eating. As a rule, if I'm going to eat it within the next few days, I just keep it airtight at room temperature (this is includes buttercreams, ganaches, fruit, caramel)....if I'm not planning on eating it right away, I individually wrap and freeze.
Thanks, POLC, I learned something.