All the city needs to do is literally nothing. Just stand back and stay out of the way. Sadly this is one of the hardest things for a bureaucracy to do.
Public transportation is a 20th century solution. If cities do nothing autonomous vehicles will revolutionize transportation wants within 20 years. Which is as fast or faster than major public transportation projects would take.
Additional housing will result in a larger tax base which will automatically cover additional schooling needs.
It's not a guarantee that self-drive for cars will not lead to more use and more congestion in cities which are not upgrading their transit.
I am hopeful for autonomous app hailed buses, but there's definitely a big chance it doesn't all work out that way, and even then there is clearly still a physical limit on how much existing road infrastructure can handle.