We don't have public transportation here, small town.
Not sure if the dogs are allowed on a subway or a bus in the big cities. I know in some places at least the guide dog of people with blindness are allowed onto the bus. Not sure about other dogs. There was a video of a pet goat got into a subway train, but I forgot where it was.
Here we have one park with a sign to tell people not to bring in dogs. It is a place for BBQ.
Most stores obviously wouldn't allow dogs to go in. Once at a small grocery store, I saw a dude left his dog at the door, but after a minute the dog went in to look for him. The store clerk didn't say anything.
Back in my university, I have seen people with dogs inside the building once or twice. Nobody ever said anything.
What are some other public places off-limits to dogs where you live?