Not "any" they are all great, but some are not best for first timers. Spirited Away, My Nieghbor Totoro, Castle in the Sky, Howl's Moving Castle, Princess Mononoke, Steamboy, Porco Rosso, or Kiki's Delivery Service are all great films for first timers.
If you really want to give them feels, go for Grave of the Fireflies. That movie is amazing at making grown people cry.
Some of the rest are beautiful and well done, but slow and relatively mundane in setting or just outright strange. I personally think his lesser known work is best viewed after some experience with Anime as a medium.
If you're going to start with Miyazaki, go big with one of his more exciting or interesting films.
If I had to recommend just one I'd say go with Princess Mononoke. It's a great example of what Anime is, hauntingly beautiful, brutal, and is simply a great example of Anime as film overall.
Barring that, if you just want to show something completely badass, do Ninja Scroll or Ghost in the Shell. Ninja Scroll is less introspective and philosophical, but it's visually amazing and brutal.
Ghost in the Shell is honestly a better put together movie though, and a better choice to show a movie buff. Someone who is really into film will appreciate the nuance and dialogue of that film more.
If none of those work for some reason, Akira. You really can't go wrong with that one for showcasing the range of what Anime can be. It's very adult and hard edged, very similar to Road Warrior in it's sensibilities. It also has moments of comedy in it and as a contrast to Road Warrior is very colorful throughout.