Take a look at Pololu.com and their Sumo bots. Maybe there are Sumo bot competitions near you.
High schools often participate in First Robotics at different levels
Could also suggest getting into NASCAR/Army sponsored Ten80 Racing challenge (remote control cars, 12-15" long)
At my son's school, the juniors compete, and the seniors from the prior year provide guidance. If his school doesn't have a team, he could start one up. They model the car, give presentations, and of course, race!
I don't think it's too late to get in to Ten80 for this season. His junior year they only got in about 6 weeks before the finals, and pulled off a 2nd place finish overall, and the school won the next year. Schools compete regionally and then at National finals. The Finals are at different NASCAR tracks, my son went to Charlotte Motor Speedway, this year looks to be at Homestead-Miami Speedway in May.
It's all good engineering experience.