The Onitsuka Tiger by Asics was originally a running shoe until it was adopted by many as a casual shoe. Most memorably, it was worn by Uma Thurman in Kill Bill (pictured above) in several different colorways.
Most of the Onitsuka Tiger models are vegan:
Gel Lyte III
A few releases of the following models are vegan:
Mexico 66 Tai Chi is the yellow model worn by Uma in the sword fight scene, while the white and blue stripe one is the 60th Anniversary edition (not vegan, unfortunately). There are way too many online vendors selling all sorts of colorways, so I won’t even bother linking to any of them. Just google it, I’m sure you’ll find something that suits you.