"What will happen tomorrow?"
Translation:Kio okazos morgaŭ?
I do not understand why kio does not take the accusative ending here. Kio is the object, is it not?
No, it isn't.
The subject of "happen" is the thing that happens - in this case, "what?".
There is no object. You can't "happen an event".
If you wanted to make it transitive, you could say "Kion mi okazigos morgaŭ?" (What will I cause to happen?) and then "what?" would be the object of "okazigi".