There is great shopping on every street in the commercial part of Beverly Hills.  Most of it is very expensive though chain stores have begun to pop up on the side streets.  Rodeo drive still only has high-end boutiques.  but if you walk one block east to Beverly Drive you will find stores like Anthropologie and Banana Republic.  On Beverly there is a lovely children's boutique called Pixie Town.  They have beautiful traditional and some funky clothes for babies and kids.  The great thing about Pixie Town is if you are lucky enough to be in town when they are having a sale you'll find some great deals.  Clothes get marked down to 50% and while they are still expensive at times, you'll get a beautiful item and feel half as guilty.  Another amazing children's store is Oilily.  They are located on Brighton near rodeo drive.  Oilily has simply amazing kids and women's clothes.  Beautiful fabrics and unique designs.  They also have fabulous sales. 

Another children's store is called Auntie Barbaras.  It is located south of Wilshire Boulevard on Beverly Drive.  They tend to be more expensive but have great sales as well. One of the keys to shopping in Beverly Hills is to visit when the seasonal clothes are changing.  That is when the deals are.

The stores on Rodeo Drive got a bad rap from the movie Pretty Woman.  Honestly though, many of them live up to the reputation.  Skip the boutiques and head to Neiman Marcus or Saks Fith Ave where it is a little less snobby.  One thing to be aware of is that if you are a woman and wear above a small size 12 you will get even less service from sales people - especially on Rodeo Drive and at Barneys New York.  

If you like designer stuff at very low prices, then go to Santa Monica, there are lots of really hip stores like DNA, on santa monica boulevard.