Rusty-James is the protagonist of this story, and his conflict is both man vs. society and man vs. self. His tendency to not think of his past or future, to act too much in the moment, is the result of his abandonment. He is raised by inept parents and in a "crummy" neighborhood. He worships Motorcycle Boy because this is the only person Rusty knows that has a plan, a purpose, and a sense of what things mean. No one else in Rusty's life - in his society - have been able to provide these things for him. Hinton is commenting in this book - as in The Outsiders and others - on the consequences of poverty in this country.
But besides the conflict with society, Rusty has to battle himself. He has to mature and to choose a path. As Steve tells him in the last chapter, when they are in fact both adults, "If you want to go somewhere in life you just have to work till you make it." Unfortunately, Rusty has not won the battle with himself or with society, and still struggles to find a place he wants to go.
The conflict of the story is Rusty James, and his fighting all of the time. It isnt good for him or his reputation.