A Arduino powered robot that has sensors. It could feature temperature sensors, photoresistors, and tilt sensors. Maybe even an ultrasonic sensor. You could use a battery power Raspberry Pi to drive a Pi Cam. Make a wireless hdmi connection wirelessly somehow. Use an old controller and an XBee to control the servos. Send sensor data to the Pi via serial use the LCD so you can see the numbers and record them. Make the Robot smart with logic via sensors. Then drive it outside.
As for the code you can use analogRead() to get the numbers from the sensors. Drive the motors somehow. Add some fun LED indicator lights(or if you are feeling up to it use the circle of light from the Xbox!).