There are so many great books in both our national literature and far beyond it. I would favor the survey format with an AP high school class; kids that age will probably benefit more from breadth than solely focusing on depth. Whether the theme is American lit (my preference because of where I live), something more local (as others have suggested), or something else
else, it's good to show students a swath of that literature and to contextualize it for them with some well-chosen additional readings, history, anecdotes, film, youtube clips, whatever.
A few other fiction texts appropriate to your student group that come to mind are Last of the Mohicans(early America), Flannery O'Connor's collected stories and Call It Sleep (mid 20th century), The Sellout, The Gangster We Are All Looking For and The Things They Carried (contemporary immigrant experience, inner-city America, war).
Those who recommended All the Pretty Horses (McCarthy's less challenging work) and All the King's Men are on to something, too.