The only place I can think of that might offer valet for lunchtime would be at a hotel, for example I imagine the Mayflower would valet, but you could call to confirm.
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 :) )
