Traffic would probably flow considerably better in a city full of self driving cars. A lot of the chaos of city driving is because of human error and human reaction delays.
You only have to fly over a traffic jam on a major highway to see problems that could be significantly alleviated by self driving cars that communicate with each other. Quite often you see traffic jams with no explanation - a mile of stationary traffic, but there's no obstacle in front and none behind. What happened is two hours earlier someone slammed on their brakes, someone following too close had to brake harder, and eventually the whole highway stops. As long as traffic is not leaving the stopped area faster than it is arriving, you get a self-sustaining traffic jam long after the original cause has gone away. The self driving car will reduce the instances in the first place of the cause, and if it does happen will be able to as a group moderate their speed in such a way that you don't end up with a mile of stopped cars. Instead of the next car only starting after it has seen the previous one begin to move + reaction delay, all cars will be able to start moving at once or nearly so.