What is "right" will depend on how you're using the nunchaku. When I was taught basic usage in Chun Kuk Do, we gripped the nunchaku about one fist width from the top. Being close to the chain reduces the "wobble" of the top of the stick you're holding and reduces the chance of the the stick getting slick with sweat and sliding out of your hand to turn into an accidental projectile. The fist's width from the chain helps protect you from pinching your hand in the chain. I think the only time we grasped lower was for the throat-strike part of our kata, where we doubled the nunchaku, grasped it close to the bottom, and then jabbed the top chain part (which often had eyelets at the top) into where the throat of an opponent would be. We never did any of the grappling with nunchaku, so I can't comment on that.
For juggling with nunchaku, the grip tends to be lower because it creates larger, flashier, movements. Juggling, and the flashy demonstrations, are also the only places I've seen double nunchaku. In general, unless you specifically train for dual-wielding, it tends to be unwieldy, and I imagine the situation would be worse with a "soft" weapon like nunchaku which tend to be less predictable, and more likely to accidentally injure the user.