Wassily sidetable  

I think Wassily's do well...
I think Wassily's do well with mixed styles .... perhaps something antique, or asian, or rustic?

again, Saarinen
Tulip table. Nothing like fluidity against geometry.

Something with a bit of wood...
Something with a bit of wood to offset the coldness of the chrome - Aalto stool (esp with a coloured top), Eames walnut stool, Breuer isokon table or better still an isokon tray table...

Eileen Gray?
Saarinen would be my first choice, but this table seems like a natural match.

...
I agree I think the tulip in black would look lovely.

The problem (for me) with...
The problem (for me) with Wassily's is the 80's associations - the Eileen Gray table would just compound this

My Wasily's are paired with...
A drum table in natural steel. My Womb chair is paired with an antique Native American chile mortar. I inverted it and it now looks very much like a Eames stool. However, it cost me $25USD and has a patina that the Eames pices can't possibly contribute. I think that kind of side table would also work well with a Wasily. To my eye the thing to avoid is too many legs. With all the tubular chrome it'll look too busy. A solid form is a better choice.

Yup, Beloved,
not much looks better next to any of Breuer's chairs than the Eileen Gray table.....a perfect match!
By the way, "'80's associations"?? Both the Wassily chair and the Eileen Gray table was designed in the 1920's! Nothing '80's about either of 'em.

Except
Except the over exposure of both pieces in the 80s. Might as well pair two LC2 chairs with a Gray table. Visual memory is going to recall that more than the Swinging 20s when they were designed.

All this
delightfully illustrates how different people see things differently, and want different things -- that is, have different associations -- with a given piece or set of pieces of furniture -- and how, therefore, there is no "right answer" when it comes to selection and pairing.
What seems natural and inevitable to one, is "too much" (or "too little," or "too common" or "too bizarre" ?) to another.
Great stuff. . .

Suggestion
Illusion side table

I agree with cebaso
I would go for something curvy and woody, though it also depends on the setting.

This brings up an interest point....
some 'classic iconic pieces'
(like the Eames Lounge Chair and ottoman,
Barcellona Chair
Wassily Chair
Eileen Gray round table
Saarinen tulip chairs and tables)
have become SUCH icons that I went out of my way to find quality living room furniture with a different spin. Instead of getting the Eames Lounge chair, I went for the Saarinen Grasshopper.
There's SOOOOOOOOOOO much good stuff to choose from (either new versions or vintage pieces), that you don't have to be quite as obvious (no offense).
I could've bought an ARCO lamp, but settled for the current Triennale-like lamp from Sonnoman.
Certainly my zebra-print Aalto tank chair is not anyone's first choice for a low chair, either.
Bottom line, there's a hundred perfectly appropriately nice tables to put next to your Wassily chair.