The most obvious reason would be that the city might be safer without motor vehicles. In today's society, cars take the lives of several thousand people each day. There's a particularly one-sided danger for pedestrians, and if drivers are a minority in the roads of California's cities then those drivers can pose a serious threat to the safety of the rest of the population.
Another issue might be found in the development of infrastructure. Depending on how badly our current infrastructure was damaged during the war, I see two possible paths of development. In the first scenario, the current infrastructure was badly damaged or destroyed by the war, leaving open spaces for the survivors to make a fresh start. Depending on the organization and planning of the cities, there may not even be roads, given that cars wouldn't have been useful for a long time after the war. In this case, there simply isn't any room for cars to fit in a pedestrian-oriented city. In the second scenario, the Californians build upon the remnants of the existing infrastructure, with roads remaining intact in between the buildings. In this case, again, the pedestrians may have simply taken over the walking space. With drivers being a minority, the pedestrians feel no need to inconvenience themselves for the sake of allowing automobiles in the city.
The people of California's cities may also distrust cars for special circumstances and plot reasons. Maybe the cars were powered by nuclear motors as in the Fallout games, and the natives believe them to still be dangerous or prone to cause explosions. If these cars are left over from before the war, there may be a sense of general mistrust for the technology and the civilization it once represented. They might even dislike cars for their pollution, which they have grown more sensitive to after the apocalypse. Overall, there are a variety of explanations that you can use to justify your prohibition of vehicles in cities.