Depends what they're into.
I got into anime through the classic 90s films like Akira, Ghost in the Shell and Ninja Scroll.
You can't go wrong with Death Note, I would say that's one of the best modern anime series.
One Punch Man and Mob Psycho 100 are good because they are funny, and have great animation and action too.
Attack on Titan is cool but I'd recommend the others that I mentioned first, just because they're a little more accessible.
There's also some weirder stuff that I love, but I might not show someone who hasn't seen anime before: NG Evangelion, Serial Experiments Lain, Mushishi, GitS SAC, Paprika, Berserk, Basilisk, Samurai Champloo, Urotsukidoji etc.
This is the best list on the thread. Alot of the commenters havent been watching anime for that long. If you havent experienced 80s/90s anime, it's impossible to make a comprehensive list. There's also Cowboy Bepop, Mobile Suit Gundam Wing (my fav gundam), yu yu hakusho, and all of Miyazaki's works (the best ones are the ones that he wrote/directed). And don't forget the original Dragonball series (not DBZ).
Also: "Your Name" is a modern anime film that did really well and has an amazing story! Regardless of their opinions on anime, alot of cinephiles enjoyed this one.