I can’t help with first hand experience but there are a few blog posts and lists on the internet that describe dog friendly cafes - for example this one and this one. Out of those though I can only remember going to the millhouse (a couple of years ago) and I didn’t bring a dog with me when I went.

It’s not in a category you mention but Bunnings appears to be dog friendly if you’re interested in a bit of hardware shopping. I see dogs in there semi regularly and the staff don’t seem to mind.