Kukata didn't go far. It was late evening, and he could still see Pride Rock from where he was standing. His ears folded back gently against his head, considering everything. He never really thought about life, just about the safety and well-being of others, especially their health. He was not able to stop a hyena from swiping at his eye. He was not able to prevent a cheetah from attacking him when he was a stray cub, nearly taking off his nose. He was definitely not able to hide the severe burn he received from a wild fire some time ago. Yeah, he is able to hide the burn, but if he were to hide his scars he'd be unable to see, for covering both the burn and the scar across his eye with his thick black mane would cut off all visibility for him, and he'd rather look like a mess rather than be blind.
Indeed Kukata was lucky to be alive. He had Rafiki to thank for this, as well as Simba, Nala, Kiara, and Kovu for giving him a place to be with his kind. His shyness around the other lions didn't help him socially, and that always angered Rafiki, but there was no doubt in Kukata's mind that he envied Kovu and Simba. They had faced family issues like himself, but were able to come out looking strong and graceful as they always had.
Kukata turned around slowly, and headed back to Pride Rock, with only the intention of sleeping on a rock behind the entrance to the cave.