Okay so, I know that the title specifically asks what books should be turned into musicals, but, I'm going to throw one out there that I think would make a great play. The Giver by Lois Lowry. It would be interesting to see how they can make the scenes look monochromatic using the lighting / clothing / makeup to make people appear black & white during a portion of the play.
As for books that would make good musicals, I do agree that The Outsiders would have a nice Grease meets West Side Story vibe, if done right.
Also, since Great Comet did so well (in terms of gaining a large fanbase - despite the fact that it closed so early), I think that Anna Karenina by Tolstoy could be a very dark and dramatic musical. I'm all for light-hearted and fun musicals, but, I do love dramas and tragedies. It would appeal to a more mature audience for sure.