Check out this list of design challenges if you are looking for an EV3 based project to explore robotics.
Design, build and program a robot that can move itself using no wheels for locomotion.
Design, build and program a robotic creature that can sense its environment and respond by moving.
Design, build and program a robotic system that follows a path and communicates its position at least twice along the way.
Make a Sound Machine that can play a rhythm, music or just noise!
Invent a Security Gadget that will protect your belongings by warning you!