Violent femmes cover of "Do you really want to hurt me?"

Go with Watchtower. Dylan/Hendrix combo covers a lot of ground.

You should perhaps consider some Who, Dead, Tom Petty and Yes ...

Watchtower is one of those songs where the songwriter (Dylan) didn't really understand the song he wrote, then another performer comes along and does it justice.

As my shaman friend puts it, The creative person's job is to be a clear conduit for the creative spirit, not coloring or filtering the transmission with their own "stuff" (for want of another term.) Dylan was the clear conduit for the song's writing, and Hendrix was the clear conduit for its performance.

Another example off the top of my head is Richard Thompson's Vincent Black Lightning. The Del McCoury band performs it so much better than Thompson.

Again, this phenomenon of the cover being more massive that the original deserves its own compilation.

I'll supply a foreigner's viewpoint.

Gotta have some Kate Bush - Wuthering Heights.
(along those lines also some Tori Amos - you could include her version of Smells Like Teen Spirit and kill two birds with one song)

On the basis of broadening his mind and including music people elsewhere in the world enjoy, I suggest an Abba track. Waterloo is arguably their most recognised.
And along those lines Weather With You by Crowded House - I'm a fan personally, but sales of Woodface were HUGE in the early 90s so it does invoke a specific timeframe for many people.

Oh and some Pet Shop Boys. In Suburbia is a great song of its time. If you prefer a cover then Always On My Mind.
Van Morrison's Brown Eyed Girl - always a dance floor filler and used in numerous films/ adverts.

I don't know if Madness were ever known over there, but it's great ska-lite. Welcome to the House of Fun, Baggy Trousers or It Must Be Love.
And along those lines The Specials - Ghost Town. Another great song from a time when city life was going from bad to worse.
Two other great songs of that era - The Jam's A Town Called Malice and The Stranglers' Golden Brown.
And talking of heroin chic, you've gotta have some Lou Reed... but I'm going back across the pond now.

And some Simon & Garfunkel (I know Paul Simon has already been suggested on his own merits) because of their glorious harmonies - The Boxer, Bridge Over Troubled Water, Feeling Groovy, Homeward Bound or Cecilia are all wonderful examples.

Great ones SG - I totally forgot Van Morrison and S & G.

"It Must Be Love" and "Our House" were both hits over here. I went through a brief but intense fangirl phase for Madness, so I have all of their albums up through about 2000 or so. "Wings of a Dove" has always been one of my favorites.

Don't forget this

Jefferson Airplane - I'd suggest Somebody to Love and Plastic Fantastic Lover the live version.

Crosby, Stills, Nash, and Young - Teach Your Children or perhaps Ohio

I'm not interested in the more mainstream hits but more of awesome B sides. Like with Jefferson Airplane I put Embryonic Journey, even though the ones you mentioned are awesome, I'm shooting for something subtler. And SG, Van Morrison's Into the Mystic is the one that made the cut, despite how great the others are. Kate bush is of course and Smells Like Tori Amos is another great one.
CSN I'm leaning towards Cathedral, but there are so many, maybe Southern Cross.

And The Cramps: Human Fly

There are many classical pieces that one should know.
Beethoven's 5th - and what it is about - and maybe 9th.
Wagner - Ride of the Valkyries.
He should know the proper name for the Lone Ranger music ;)
Carmina Burana
Brahms Hungarian Dance no 5

Oh and Dave Brubeck Take Five - what is it with the fives? :)

The fives go up to eleven. ;)