For christmas this year, I got a Raspberry Pi. It’s a small little single-board computer that were originally developed to help teach computer science, and are now also used by hobbyists to build games, robots, whatever.
It’s pretty easy to get started with a Raspberry Pi, in fact the whole site seems to be geared towards children! You just buy the little Pi, install the software onto an SD card, then plug it into power, screen (e.g.tv), mouse and keyboard. There is also a port for an ethernet cable if you want to get on the internet.