Originally Posted by Platy
A fully functioning car free city would be a pretty tall order.
What might be possible would be for an older small town on a major recreational trail to become a popular destination for recreational cycling and hiking. If the concept worked well, some regular visitors might become year-rounders. It might develop along the same lines as an artist colony.
Platy... I think this kind of exists already. There are some trails in Minnesota and Wisconsin that seem to fit your description. They aren't car-free yet, but it sounds like the next evolution for them.
http://www.rootrivertrail.org/lanesboro-main.php