Very good suggestions.
When you wrote The Invisible Man, I thought you meant the book written by Ralph Ellison which is a great book. A bit long.
Shorter and very readable (I read it on a 5 hour transcontinental flight): The Heart is a Lonely Hunter by Carson McCullers. It is character-driven and compelling. Description by Wikipedia:
The book begins with a focus on the relationship between two close friends, John Singer and Spiros Antonapoulous. The two are described as deaf-mutes who have lived together for several years. Antonapoulous becomes mentally ill, misbehaves, and despite attempts at intervention from Singer, is eventually put into an insane asylum away from town. Now alone, Singer moves into a new room.
The remainder of the narrative centers on the struggles of four of John Singer's acquaintances: Mick Kelly, a tomboyish girl who loves music and dreams of buying a piano; Jake Blount, an alcoholic labor agitator; Biff Brannon, the observant owner of a diner; and Dr. Benedict Mady Copeland, an idealistic black physician.