In the urban areas.
I'm in Manhattan on a regular basis as I have an office there. It's pretty much taxis, limos and Uber/Lyft service there already. I know some brave souls do it but it's crazy to take your personal car to Manhattan. Everything about driving in Manhattan is a nightmare from the constant gridlock, avoiding jaywalkers, navigating the various one-way streets, jockeying for position with the trucks and the double-length city buses and of course, the parking, in which you almost always have to hand your keys over to a guy who looks like he just got out of prison and then pay in the neighborhood of $50 to get it back a few hours later.
So I see it happening there first. Private cars banned. Self-driving taxis. You plug your destination into an app on your phone and the next available pulls up to you (flashing your name on top) and you step inside. You are taken to your destination and your credit card is being debited for the trip. No tipping unless you want to give the car a little rub and tap on the way out. For the poorer people, well, you need to rely on the city buses and subways.
It's happening. For better or for worse. Brave new world. There is nothing we can do to stop it.
Of course the city busses will be driverless too, as well as the subways, I mean why not?