In chapter 5, what traditional dichotomy does Hawthorne begin to establish with the location of Hester's cottage?

I'm not sure what you mean by traditional dichotomy except that I see a free person inflicting bondage upon themselves.

Hester could have left this town and the shame of the reputation she had come to acquire. But no, she chooses to stay:

Here, she said to herself, had been the scene of her guilt, and here should be the scene of her earthly punishment; and so, perchance, the torture of her daily shame would at length purge her soul, and work out another purity than that which she had lost...

The "here" she referred to is this New England town. Her cottage was indeed on the outskirts, but it was an abandoned place which the magistrates were able to keep an eye on. Thus it became another sort of prison.

This woman is free but keeps herself imprisoned and under punishment. That is a dichotomy because what free person would want to be confined? A Puritan one would. Puritans were good at accepting the consequences of sin, but not the forgiveness of it.