For everyone praising Your Name, I do think that movie is excellent, but I found the actual best anime film around that time to be A Silent Voice. It is NOT a light film (for those who mentioned showing anime to their family) as it covers extreme levels of bullying, suicidal depression, isolation, etc. but through all the pain the cast go through and the cruel actions that the main guy makes as a child that he seeks atonement for but questions deep down if he can ever be truly forgiven, it does end on an extremely satisfying and heartwarming note.
I even had a friend I knew in college who went on to become a sign language interpreter, and many years later she told me on Facebook this film got her into anime.