In summer rain, I just generally go with either sneakers or my leather sandals, preferably ones with a bit of platform to keep me out of the worst puddles. No suede or anything delicate, of course, and nothing very flat.
However, I am reminded that years ago I got stuck in a total downpour in my beloved strappy LD Tuttles…and they survived just fine!
If it were cool enough to wear jeans/pants, I might do boots like the ones here in my Finds, if I were going to be out and about on city streets.