Breakfast near Runyon Canyon (post hike)?
There's nothing too too close to there.
Some options include:
To the east there's the 101 Diner on Franklin
South to Doughboys or Ammo on Highland
LuLu's down near La Brea & Beverly, or BLD just west of there.
West on Sunset to The Griddle or Jinky's or Mel's
Or you can do it right and head to Hungry Cat for a serious brunch.
Of course most of these will involve a good wait on a Sunday mid-morning. Hungry Cat and Ammo might take reservations, if you go that route.