Forget boring Hillsdale Mall or snobby Stanford Mall. Burlingame Ave is the most pleasant shopping district on the peninsula. It has the usual suspects such as BabyGap/GapKids/The Gap, Banana Republic, Janie and Jack, Gymboree, Pottery Barn, A Pea in the Pod etc. But it is also chock full of nifty boutiques and cool designers. Some of my favorites include the hip and adorable Peninsula Breastfeeding Center and GumShoe (kids shoe store). I have reviewed my favorite shops separately.
Unlike Stanford Mall or Hillsdale, you can actually get a decent bite to eat at one of the myriad fabulous cafe's and restaurants that line the street.
If your kids need a break, let them blow off steam at the tiny J Lot Playground (Conveniently located across the street from GumShoe and next door to Anthropologie).
Or, cross the train tracks and let them go wild at Washington Park.