Bud begins the story in Flint, MI. The story ends with him in Grand Rapids, MI, but I don't think that your question is only asking about the physical start and end settings.
When the reader is introduced to Bud, he is living in an orphanage, and a new family has just been found to adopt Bud. Right from the start of the story, it is clear that Bud does not have a permanent home or a loving family. The Amos family doesn't end up being either of those two things, so Bud decides to strike out on his own and track down his father. He scrapes to get by, has some successes, has some setbacks, and he eventually makes his way to Grand Rapids. It is there that he meets Herman Calloway and his band. Bud believes that Calloway is his father, but it turns out that Calloway is Bud's grandfather. Although the story did begin with Bud being without a family and a home to call his own, the story ends with Bud finding both in Calloway and the rest of his band.
Bud is able to achieve his happy ending through a mixture of luck, skill, and determination. Bud is extremely lucky that Lefty Lewis is the man that found Bud on the road that night. There could not have been a kinder man than him. The Great Depression is in full swing, so it's possible that the car that pulled over for Bud contained a "bad guy" looking to rob Bud of all of his possessions. Instead, Lefty Lewis feeds Bud, takes him to his home, and drives him to Grand Rapids.
Bud shows skill at times too. For example, Bud's repeated use of the library to obtain information to help him succeed shows resourcefulness on his part. Additionally, the book is full of Bud's rules that help him to better survive and navigate the dangerous world that he inhabits. Bud skillfully applies each of those rules to cleverly maneuver various situations.
Lastly, Bud shows a dogged determination throughout the novel. He is unwilling to give up. This is especially evident when Calloway clearly shows that he wants nothing to do with Bud, yet Bud remains persistent in his efforts to win over Calloway. Bud wins the hearts of each band member one by one, and eventually a situation is presented that teaches Bud and Calloway their true relationship to each other.