One of my favorite films has to be Bunny Lake is Missing. Any movie that combines Keir Dullea, Noel Coward, Laurence Olivier, and The Zombies is worthwhile in my mind. Not to mention a poster designed by Saul Bass!
I would plan a Keir Dullea Disturbed Young Man Double Feature starting with David and Lisa and then Bunny Lake.
Fear not, none of these captures reveal any spoilers. Enjoy!