I have a student/friend who's drawn to jazz, which is rather beyond my pay grade. We're just doing her favourite Laufey song, which being a soft jazz ballad is relatively easy for me to sus out and show her.

She also suggested Disney's "Everybody wants to be a cat" which is more trad jazz (to my ears) and quite a lot of fun:

^ But ... it's actually quite tricky to get into from a standing start. I've just got my fingers around the chord changes, but it'll be a bit of a reach for her. We can work on the structure, but will have to take time to build speed.
Can anyone suggest some trad jazz standards that have that feel, but are a bit more accessible?
Comments
Get them a Real Book.
(Pretty much) any jazz tune can be played at different levels of complexity.
I get people to start with a jazz standard in C, something like 'All of Me' or 'Satin Doll'.
You don't have to try to play the whole thing in one go, just take it section by section.
First level is to comp the chords along with the track.
Start to explain what a ii V I is, why it is so important.
Then have them learn the head/vocal melody.
You can simplify it as needed.
Then have them start to outline the 3rd and 7th of each chord as they play through it.
You can show them practical uses for arpeggios by doing this, rather than a load of rote learning that will bore them.
Teach them how to circle notes (semitone above/below) and when to use it.
You can also explain how to make a minor lick into a major lick- all the usual stuff.
It can be weird what someone latches on to so it can sometimes help to be a bit scatter gun about it.
Throw some things out and see what sticks.
The thing that really fired me up to learn was when someone explained to me that you could use a diminished 7th chord in place of a dominant chord by sharpening the root of the dominant chord.
So G B D F = G# B D F.
And when I learned you could slide it about by minor 3rds.
I just thought it was the coolest.
That little bit of information was really what got me interested in jazz harmony.
If this isn't something you've done before then it might be great for you as well- you only really need to be a few steps ahead of them to teach it. Although I'd probably come clean about it and say 'this is something we can figure out together, if you want'.
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@octatonic - she wants to remain theory-lite. Mainly because she has picked up a guitar to de-stress from her academic job. So she doesn't want to think consciously beyond remembering what to play. So any significant theory gets in the way.
I am learning more theory these days (Bennett, Beato, etc), but the days when she is keen to learn about secondary dominants, line cliches and other fascinating stuff are way ahead.
Theory doesn't have to be scary, or complex.
Anyway, if this is a definite thing then I guess the way to do it is just going to be comping the chords and then teaching her to play the melodies by ear.
Satin Doll and All of Me are good choices, but really I would ask her what she likes.
I might consider transposing out of difficult keys, but if she isn't reading and it really is just copying what you are doing then it might not be an issue.
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