Policy reader in the house
Couple of things would happen here. First line would be if the valet service has its own policy, then it would be paid under the Garagekeepers portion of the policy as the cars are in their care, custody or control of the valet company. If this is the case, then they were technically in the business of "transporting" or "parking" the vehicle. At least that's how I would try to explain it to the insurance company. The ISO form isn't specific enough regarding this.
If the valet service doesn't have this coverage, then it may fall to the restaurant if they've contracted out, but I'd put my money on them not having coverage on their policy for stuff like this.
Lastly, the personal auto policy would respond to this ultimately. The car wasn't being used in a racing capacity, or something along the lines of that exclusion, and a personal auto policy is pretty broad in its scope of coverage.
EDIT: Kid is a retard