If you like Hitchcock, he had tons of other movies, like North by Northwest, Strangers on a Train, Rebecca, Notorious, the Birds and The Man Who Knew Too Much. Also anything from Agatha Christie, like Alibi or Ten Little Indians from around the 60s, or And also , Then There Were None and Murder Most Foul, from the 40s.
If you like cool fun movies from back before SJW, then anything with the Rat Pack, and also Some Like It Hot and the Seven Year Itch, and Bedknobs & Broomsticks. and even Singing in the Rain. If you like lighthearted movies, then you could look to the Elvis movies from the 60s like Viva Las Vegas or Blue Hawaii or Love Me Tender. Most of these movies all have a decent amount of music involved and could be called musicals.
Another idea is the old spy/thief/con movies, the James Bond movies with Sean Connery like Dr. No, Goldfinger, or You Only Live Twice ( plus many more ) from 50s or 60s. There was also an original version of To Catch a Thief" with Ryan O'Neal in his younger days. He had a likeable snark about him similar to a Nathan Fillion today. Also, Paul Newman in his The Hustler movie.
My last suggestion is pick a coupe of actors from the those decades that were huge back then and google for their movies. Cary Grant, Rock Hudson, Tony Curtis, Shirley Maclaine, and Doris Day...etc.
It is really cool to see how well some of the premise on the movies still ring so true today, a good example is All About Eve, you might recognize the plot as it has been "stolen" by many newer movies through the ages. This is probably true of most of the true classics from the past tbh.
Whatever you do decide to watch....Enjoy!