The problem with most suggestions for advanced materials is whether they could be grown and repaired by a biological system. Many are not at all biologically compatible: embedded in a body they corrode or cause inflammation or other adverse immune responses. We can make bone replacement implants from titanium and certain ceramics. Our biology tolerates these but cannot maintain them, and more surgery is needed when they wear out. Much medical research is directed at how to create a temporary framework that can be seeded with bone cells and implanted, to grow into natural bone with ultimate metabolism and elimination of the framework.
Bone, as already mentioned by others, is comparable to.mild steel for its strength to weight ratio. It is also a living tissue, continually repairing itself so that micro cracks do not propagate into fractures (c.f. metal fatigue!) It can grow, repair after severe damage, strengthen in response to repeated heavy stress. Hundreds of millions of years of evolution may have produced the optimal skeleton.
What about plants? Different requirement, different solution. Wood. Cellulose fibers bonded with lignin. Again, can be extremely strong. Now we have artificial glues to match lignin, we can re-form wood into "glulam" beams, which are pretty much the equal of structural steel. Interestingly heartwood is not living tissue. A tree protects it from external attack with a skin of living tissue, but in most mature trees it is rotting in the centre. Which does not matter to the tree, or which may even be of benefit. A cylinder is as strong as a solid trunk. As the core of the trunk rots, nutrients that were locked up in the heartwood are released back to the tree's roots. Droppings from creatures that take up residence in the trunk provide more nutrition. Eventually of course rot gets the upper hand and the tree dies if it cannot regrow from its roots. Death is part of nature's plan.
Insect exoskeletons and fungi use chitin, yet another remarkable biological material, though one better suited to small elastic structures than large ones.
In short, I think it likely that the materials evolved for skeletons cannot be bettered by purely biocompatible processes.