The Circuit Playground from Adafruit is certainly an interesting little board. It comes in the shape of a disk, can be programmed with the Arduino IDE. In addition to other features, it can produce sounds, has programmable LEDs around it, and can detect taps. You can get this little guy for just under $20 on Adafruit, or for $25 plus shipping you can get it from Tindie in the form of the NeoPix Arcade kit.
This system takes advantage of this board’s capabilities to create a 1D pong game. The ball (light) bounces around the circular disk, and for control, you simply tap on the cardboard box on which it’s mounted. The kit can be programmed to play other games or be used in other applications, and since it comes with a battery holder, and comes pre-programmed with this game, it looks like a good place to get started with electronics tinkering.
You can see more details on this build and the code used for this game here.