The Stockholm Shopping Guide website lists the shops for children's items. Another shop featured in a New York Times article in April 2011 is Morkarin. Visit Stockholm Blog (on 8 July 2011) recommends Kalikå in Gamla Stan. And Livly at Birger Jarlsgatan 9 is another good place to go.
Among these shops, my personal recommendation is Sprall. Its website is in English. See this page for the store locations.
The Moderna Museet, Stockholm's contemporary art museum on the isle of Skeppsholmen, has a gift store in which you can buy intellectual toys for kids (according to the Shift City Guide).