From the book The Road
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The man and boy are traveling south, towards the sea, because they will not be able to survive the winter where they are. They are traveling through a post-apocalyptic world covered with ash and without animals or plants to eat. They are hoping to find a warmer climate, a better situation, safety, and food. While they eventually reach the sea, their situation does not improve, and the man dies. A very depressing, but very beautifully written book.
WE are never given a destination. They are moving South towards the ocean. They are looking for something more. They are hoping to find some more "good guys."