Huck's desire is to be free. His conflict is also related to freedom in terms of morality and moral thinking. Huck's dreams, however, are less specific and more negatively defined than his counterpart Jim.
Where Jim wants to reunite with his family and live a life with them in Ohio, Huck only knows what he does not want.
He does not want to live with his father (who might kill him and almost has already and who wants to take his money). He does not want to be constantly in school and in training to become more civilized either. Though he comes to like the widow, the strictures and structures of life there often lead Huck to repose to the wilderness.
In nature, he finds solace, but he does not necessarily dream of being a woodsman. Unlike Tom Sawyer, Huck also does not dream of adventure. Huck is a person tortured by the compromises forced upon the individual in society. He strives to come to a clear understanding of how to be an individual, how to maintain integrity, and how to get along with others all at the same time.
If this is his problem, we might say his dream is simply one of an escape into simplicity and reduction of conflict.