Seconded, I loved that book.
Two of the books I remember from my modern American lit class were *Ellen Foster and The Bean Trees. The Bean Trees touches on child/sexual abuse and racial issues, but not nearly as explicitly as The Bluest Eye.
What counts as “contemporary”? Steinbeck is accessible to all ages, The Grapes of Wrath if you want length, Of Mice and Men or The Pearl if you want something brief.
Arthur Miller’s The Crucible is popular and deals with complex themes without being too dark–the sexual stuff is all implied, and the older ones will see it but the younger ones will still get plenty without it.
Speaking of drama, Lorraine Hansberry’s Raisin in the Sun deals with race issues with insight and power while staying fairly PG.
Tim O’Brian’s The Things They Carried is a popular contemporary work among high school teachers these days, but I haven’t read it.
I read the first chapter of that one in a lit class. I really liked it. I second this one.
I Know Why The Caged Bird Sings
Go Tell It On the Mountain
I seem to remember both of these fitting that description from an Africian American lit class I took in college (we did make fun of The Color Purple though)
On the same lines, but not racial is A Tree Grows in Brooklyn.