Maybe some Dave Brubeck? Strange Meadowlark is nice, Blue Rondo alla Turk is pretty iconic.
I second Gershwin, currently agonizing over "I Got Rhythm" right now...but there are easier arrangements if you like.
Slightly less "on-point" might be some ragtime? Joplin or Botsford would be the obvious choices, and this is an important precursor to jazz.
I also like Robert Starer's "Sketches in Color" for introductory-to-intermediate-semi-contemporary selections. "Pink" and "Orange" are pretty popular, you can find them on Youtube.