Car free shopping districts and streets are common worldwide. Even the US has them. Pennsylvania Avenue in front of the White House is open only to foot traffic and bikes. The only cars in there are emergency vehicles. Charlottesville, Virginia has a pedestrian mall.
>Europe generally doesn't have the sprawling suburbia of the eastern United States that would require massive ring-roads to handle traffic that isn't feasible to serve via mass transit
The sprawling suburbia of the US comes from poor land use policies that do things like require single family housing. This is true even in cities which are famous for not having zoning, like Houston.
Before we engaged in the Great Suburban Experiment the US was one of the world leaders in public transit. LA had one of the largest public transit systems in the entire world.
Loosening certain land use controls would slowly repair this problem amongst many others.
Lately these laws have attracted a lot of attention in the press, with economists from Paul Krugman on down commenting on land use controls, mostly negatively.
Cities are slowly reforming these laws, or attempting to reform these laws, and I suspect that the America of the future will be much more walkable nationally than today's America. Even LA's leadership has realized that the car doesn't scale.