There probably isn't much valet parking provided by resturants at lunch. There are plenty of garages in the area that will park your car for you in their facility for a short duration. Dinner time has many more valet options since the garages and lots empty out.
Mio has detailed parking info during lunch hours since they don't offer a valet during the day. Check out their website (and if you go there report back since I'm thinking of trying it soon but there doesn't seem to be a whole lot of Chow reviews out there :) )