One of my favorite places to have lunch here in LA is definitely Villa Blanca in Beverly Hills.
Nothing like bringing your best girl friend out, order some nice appetizers and a glass of wine and chat for hours on the nice patio and watch everything from people in nice suits and elegant dresses, to lost tourists and the billionaire widows in fur coats in a boiling 90 degrees walking by.
It is always excellent service and really good food.
So bing your dark shades (you know, so you can stare at people without them knowing), your best friend and a couple of credit cards, you might stay for a while.