Anybody who has a kid with Autism and has had Occupational Therapy has probably been shown the wonders of sitting on an exercise ball for their child. We've had one for years down in our basement, although it's probably about 3 feet wide, pretty large. We've had fun over the years letting him lie on his belly over it, and while holding his feet, let him push off the floor, sorta like doing "push ups" or sitting him on top while we held him and bounced him.
But, now that he's about 5'2 and 116lbs, it's a little more difficult to do such activities! My sisters in Indiana being the work out mavens that they are both have exercise balls that are a bit smaller, and somehow he always finds them when we visit, and loves to bounce himself. It's great proprioceptive activity, and very calming, yet an energy burner at the same time.
I finally bought one for our house and it's a hit. I totally suggest one for any kid, especially when they're watching TV. He sits on one at school as well while working. Even better, it cost 10 bucks at Walmart!