It depends on how far the fall is, and what angle you hit the ground.
The highest recorded G's that a person has experienced and survived was when Kenny Brack crashed into Tomas Scheckter. It was 214G, which is about 2097 m/s^2. According to this calculator that's equivalent to something like a fall from 80 meters with 4cm stopping distance.
Kenny Brack suffered multiple broken bones, but the wikipedia article doesn't list any internal injuries, so I'm going to assume that his only internal injuries were related to the fractures. I assume his flesh experienced almost the same G force that his bones experienced, so I would take this to mean that a person could remain relatively uninjured up to that point.
So, yeah, if I'm not terribly mistaken, then a person with unbreakable bones could stand up to about an 80 meter fall with minimal damage, if they landed the right way. Depending again on how they land, a fall from as low as 10 meters could give enough G's to knock them unconscious.
I want to note, against some anticipated objections, that unbreakable bones does not mean that the person will be perfectly rigid on impact. The person's joints will still bend in the normal way, cushioning the impact only a little less than what you'd get with bones. Eventually, though, if the fall is from high enough, that small amount of cushion you get from your bones breaking will make a difference and save your internal organs. I don't see any good sources online about where that cutoff is, but I wouldn't want to test it any higher than 80 meters.