Charade

 It's hard to avoid Charade. It's on TV all the time, on Netflix WI, and has been public domain forever so you can watch the whole thing on YouTube. Plus, I own the world's crappiest copy of this movie, purchased for $1 at Walgreens, that you can borrow anytime. Boy, it's a weirdie but goodie!

A really harsh murder mystery mixed with a refreshingly self-aware May-December romance and a handful of screwball comedy thrown in, its tone is so off that you just have to keep watching to figure out what the heck they're trying to do with this movie
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With added Coburn (and Matthau!)

 I'm not a fan of Breakfast at Tiffany's (sue me!) and actually think this is the most fun and fashionable Audrey Hepburn movie! I also like to imagine that this was filmed during Cary Grant's LSD experimentation phase. Watch the incredible opening titles accompanied by a classic Mancini jam and pretend you've been prescribed a little acid for your mild anxiety (read this great Vanity Fair article, "Cary in the Sky with Diamonds," for the deets on early free n' easy LSD use in Hollywood and psychotherapy!)