Nathaniel Hawthorne came by his knowledge of the attitudes and beliefs of the Puritans naturally; he was a descendant of John Hawthorne, a magistrate during the Salem Witch Trials of 1692.

Puritans tended to believe that the woods should be avoided for both practical and spiritual reasons.  Practically speaking, the woods were a place that concealed the Native Americans who compromised the Puritans' safety.  Puritans had little understanding of the indigenous people's spiritual beliefs and, thus, dismissed them as devil worshipers; as a result, the woods were a place where a Puritan should not stray. To enter the woods was a symbolic act of exploring life outside the orthodoxy of Puritan belief, making it the perfect setting for Young Goodman Brown to put his faith to the test. 

Salem was a colony set up as a religious utopia for the Puritans. Like its predecessor, Plymouth, Puritans believed that they had built a model "city on a hill," a new Zion that offered a model for other Christians, especially the ones they considered tainted, namely, the Quakers, Anabaptists, Anglicans, and Catholics. In "Young Goodman Brown," Salem represents a stronghold of faith. The fact that the titular character elects to step outside it—and suffers terribly as a result—suggests the intolerance, rigidity, and ultimately unrealistic nature of a religion that demands perfect conduct from its practitioners. 

I would also add that the woods are uncertain, secluded, secretive, and full of different types of things that lead to many possible things occuring there. Hence, his journey into "the woods" also represents a journey into the forces of evil which can be easily described as the woods themselves.

The fact that the story begins and ends in Salem is a symbol of the starting point, and then the endpoint of his life after his "visit" to the woods. Salen is hence the safe haven (which we know its sarcastically put in the story), and the woods are the plunge into sin.