All the Bright Places by Jennifer Niven
When Theodore Finch and Violet Markey meet on the ledge of the bell tower at school - both teetering on the edge - it's the beginning of an unlikely relationship, a journey to discover the "natural wonders" of the state of Indiana, and two teens' desperate desire to heal and save one another.
If you want another character-driven, emotionally intense young adult novel, try one of these.