What did Joe want to do more than anything in A Long Way from Chicago?
I believe what you are asking about is Joe's longing to learn to drive. He looks upon driving as a rite of passage, and though when Grandma asks him why it is so important, he can't exactly explain it, he thinks,
"I was getting too old to be a boy, and driving meant you were a man. Something like that."
Ray Veech, who is "seventeen and man-sized," has given Joe a couple of driving lessons in the past, but he wants two dollars for "the full course," money which Joe does not have. In addition, Veech's garage has a "showroom-fresh Terraplane 8 from the Hudson Motor Car Company" in stock, and when Joe sees the car, it is "love at first sight." The Terraplane is the same model that the infamous Dillinger drove to get away from the police, and Joe is determined not only to have the driving lessons, but to drive the Terraplane as well.
Joe manages to get the money, and on the evening that he goes for his first lesson, there is "a song in (his) heart." Joe feels like he is "six feet tall and shaved," and even though his shining moment is slightly sullied by the fact that Grandma insists that she and Joe's sister go along for the ride, he greatly enjoys driving the Terraplane, which he believes is "about as fine a car as they'd ever make" ("Things With Wings - 1934").