It’s a tough question, because I don’t think there’s any one opera that sums up the art form, nor any one composer, period, nationality or style.
So, part of the challenge is to expose someone to an art form which seems to have a binary response - you love it or you hate it, with not much in the middle.
Not to answer a question with a question, but what sort of classical music does your friend know and like? Only a couple of composers? Lots? Different periods or only one? I’m asking because it may be a better match to figure out how to see an opera by a composer that you know your friend enjoys.
Elektra or Salome? Well, they’re strong dramatic pieces, but even for Strauß they’re kinda heavy going. It’s like Wozzeck - Wozzeck is also only about 90 minutes long, but it feels a lot longer because of how intense the musical and dramatic journey is. If you like it, that’s a good thing. If you don’t, well, I don’t know, you walk out, I suppose.
Of the Mozart operas, I’d go more for Marriage of Figaro or Don Giovanni. Magic Flute is rather heavy going - the plot has that weird switch and bait of Good vs. Evil, and Sarastro is just a crashing bore. Don Giovanni is more interesting if you can just skip all the bits involving the goodie-goodies, but of course, that’s not the point.
Peter Grimes is a good recommendation; may I throw in Albert Herring? If it’s directed well, it’s a very funny satire of British village life, and the whole idea of the protagonist getting drunk and telling all these pretentious busy bodies exactly what he thinks of them all is priceless.
I do think you’re much better off to go see something live and in person - it’s so much more impressive to have the distance between you and the stage and to see how the whole picture unfolds. I’ve seen lots of opera on DVD and it just leaves me cold.