ナルキッソス～もしも明日があるなら～Portable

The anonymous protagonist is diagnosed with a terminal illness shortly after his twentieth birthday, and is admitted to a hospital in Mito, Ibaraki. There he meets Setsumi, a woman a few years older, who is also terminally ill. Finding that they both reject to die either in hospital or at home, they steal a car and run away together. [Edited from Wikipedia]