Living in a US city that has no cars for personal transport
Venice probably is the only place that matches that criterion.
On Malta, there also is Mdina, which is largely car-free but still allows for limited car usage by residents. Still, although it's called a city, at a population of less than 1,000 it doesn't really qualify by any modern definition of the word.
As for the US there's this list, for example: https://en.wikipedia.org/wiki/Category:Car-free_zones_in_the...
However, probably none of these places could be called a city in the narrow sense of the word.