Point of order. The esteemed Capt. Cook didn't discover Terra Australis, he was just the first European to 'claim' it. The Dutch beat him by ~160 years, hence the name 'New Holland'.
It's unlikely that Cook ever had a grave, known or otherwise;
"The esteem which the islanders nevertheless held for Cook caused them to retain his body. Following their practice of the time, they prepared his body with funerary rituals usually reserved for the chiefs and highest elders of the society. The body was disembowelled, baked to facilitate removal of the flesh, and the bones were carefully cleaned for preservation as religious icons in a fashion somewhat reminiscent of the treatment of European saints in the Middle Ages. Some of Cook's remains, thus preserved, were eventually returned to his crew for a formal burial at sea."
Attempting to kidnap an Hawaiian king was probably not one of his smartest moves!