Many traditional explanations of conflict include things like Man vs. Man, Man vs. Nature, but these don't seem appropriate for "Young Goodman Brown." The conflict in this story is between man (Brown) and his unreasonable demands on other people to be what he wants/needs them to be.
You always have to remember that we have no solid evidence that ANYTHING happened in this story; the end seems to suggest that it was all a dream, our "common sense" seems to suggest that it's a dream, but it doesn't make any difference. Brown comes back to town unable to accept what he perceives to be the "evil" in the people he once admired---but there is no evidence that any of them are evil, just not perfect.
So the best conflict may be Man vs. Illusions.
The Enemy of the Good is the Perfect.
(I guess I should use "Person" in all of these :) )