 If you liked
Sennen Joyuu
|
 ...then you might like
Suzume no Tojimari
|
Both has a similar beggining of a girl meeting an older men and helping him, which changes both of their lives
High school girl bumps into long-haired college-aged guy, changes her life entirely from that point on, carries his key around constantly, LOTS of running, doors, earthquakes, disaster and loss...