What are the best robotics for kids?

I’d say start with LEGO, then LEGO Mindstorms, then VEX contests, then Arduino.
Speaking of which, have you heard about Mindstorms’ EV3? It adds iPhone and Android support out of the box. http://www.theverge.com/2013/1/7/3845222/lego-introduces-android-ios-compatible-ev3-mindstorms-robotics

I wanted to connect my iPhone to my Arduino robots two years ago but Apple wouldn’t give me access.