Although there are plenty of children being pushed around Beverly Hills in carriages, it isn't really a child friendly city.  Most restaurants aren't set up for kids.  There is a Cheesecake Factory which is a chain restaurant and the Beverly Hills location is incredibly noisy so that helps mask the noise of kids.  There is a fast food restaurant named Sharky's that has a great back patio for kids.  There is a small fountain and it's open to the outside.  No one ever sits back there so it's a great place to hide.  Both of these restaurants are on Beverly Drive between Little Santa Monica and Wilshire Blvd. 

The shops on Rodeo Drive are not for kids.  You will get dirty looks when you enter them and then be ignored after that.  The sourrounding streets are a bit friendlier. There is one toy store in the area that has a nice selection but indifferent service.

The one thing that is a gem for kids in Beverly Hills is Roxbury Park.  it is located on Roxbury drive just south of Olympic Blvd.  It is a large park with fabulous play equipment for kids of all ages. It's also pretty quiet and a nice place to sit and relax.