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.
Best list I see, don't forget cowboy bebop too