I think I would recommend Escaflowne for a first timer. That was one of the first animes I ever watched, and the english dub is half decent. Of course it could be much better, but I'm not sure someone who isn't an anime fan would want to watch an english dub. sweatdrop
But it's something with some action, romance, and an interesting enough plot. It's what got me back into anime, so maybe it could help other people.
I would also recommend Princess Monoke and Spirited Away. Those were two movies I showed my mom, and she doesn't care for anime, but she loved those movies. The Cowboy Bepop movie was another one she liked, though I had to explain some stuff so she could fully understand what was going on.