“Patterns” by Paul Simon is G Em C D
Forgot about that one. Maybe the student can branch out a little? 
Rocking in the Free World
Verse=Em-D-C
Chorus=G-D-C
Yeah, A7 is easy to finger and so is D7 and G7. On the other hand, F and Bm and F#m were always difficult for me.
Isn’t F generally considered to be the Chord from Hell? I seem to remember hearing that Joni Mitchell took up open tuning specifically so she would never have to play an F.
Two I’ve been playing recently which come to mind are:
Groovin’: G - C etc.
and
A Change Is Gonna Come (G a e) = the a minor can be also thought of as a C, probably, although away from the keyboard it’s hard to hear it for me. I usually play it in Bb, so maybe my intuition isn’t even close.
Blackbird is usually done in G – the chords are kind of f—ed, pardon my French, but the harmony is right around the four chords mentioned in the title with some passing chords.
All those are old tunes, though – I don’t know any hipper ones.