It's not like Mother's Day where there used to be special brunch reservations. But on any day where families typically get together you see an uptick in attendance in late morning/early afternoon when people have finished their celebration and then if they all have APs they'll go to the parks.
Carthay in DCA has a burger at lunch, and Steakhouse 55 in DLH used to have a burger, but maybe there's something on the regular steakhouse menu he'd like. Also look at the PCH Grill dinner buffet menu, they have pizza.