Depending on where you're eating and who is with you, you might not be finished by opening time. For example, if you're having a character breakfast - particularly a princess one - then it will be drawn out as you wait for refills, since they're not buffets.
As for what you get to do, I don't know. It will probably depend on the park. I would think you might be able to wander over to some of the rides and wait for FP.
But, really I don't know. I'm looking forward to the answers from those with more experience and certainly more knowledge than I.