I have not been specifically Ohio to CA, but a few thoughts that will hopefully help -
You mention central coast, which makes this suggestion a bit difficult, but many years ago I drove Minneapolis to San Diego Christmastime. I/we intentionally drove far south first and then west. Idea was to avoid driving mountains in a car in winter. I'm sure it would have been beautiful, but potentially a bad drive.
Cities/places worth stopping for a night, especially kid oriented? I don't have specific ideas other than check out this website:
Roadside America - Guide to Uniquely Odd Tourist Attractions. You can find a bunch of "roadside stops" that may give you ideas, perhaps some of them more to let the kids get out of the car and run around more than anything.
Okay, one idea - I'd probably find my way to the Grand Canyon...even if you do just the bridge and stay at the top - it's still pretty awesome.