Into the Wild follows the true story of Chris McCandless, who left behind the comfort and safety of his life as a college student in order to travel the United States. After giving away his college fund and cutting off contact with his family, McCandless traveled through the West, hitchhiked to Alaska, and attempted to survive in the wilderness on his own. He made it approximately 113 days into this odyssey before dying of unconfirmed causes.
Thus, I would argue that Chris McCandless' goals were to embark on a journey of self-discovery, to clarify his own identity outside of the superficial and often consumerist context of society, and to grow closer to understanding the meaning of life. His quest was toward enlightenment and minimalism, and he was clearly influenced by the Transcendentalist value of individualism.
Given that you are only reading about him from other people's accounts and from Krakauer's own biased view of his life, it is difficult to decipher exactly what Chris' goals were.
He clearly wanted to escape some of the bounds of regular society that he felt held him back from perhaps discovering his true self or perhaps even being truly happy. He finds companionship and things that are worthwhile in working for people and finding those folks that he doesn't find to be fake or untrue, but he also quite actively works against people getting close to him, whether they are family or friends.
One other goal is simply to push himself to a level he likely can't himself so escaping to nature may bring those challenges to him.
Id say his main goal througout the story would have to be the last two questions on the end of page 172.
"Who are we? Where are we?"