The oldest cities in the US generally have the best public transit, as they were developed around walking and transit before cars were widespread. They are generally on the East Coast. In many of these cities, libraries and parks are within walking distance anyways, and there are some neighborhoods where downtown is an easy walk away as well.
I live in New York City. The majority of families don't own cars here in the city, and traffic is sufficiently congested that driving is usually slower than mass transit. The subway runs 24 hours a day. You can take various forms of public and private mass transit to pretty much any point within 50 miles, and many far beyond. Most neighborhoods have a park and library within easy walking distance, as well as a shopping street with supermarket and grocery stores. There are tons of excellent jobs here, but unfortunately there is a pretty severe housing shortage and apartments are ridiculously expensive-- a room in a decent neighborhood is often $1000+.
Chicago likewise has an excellent and extensive mass transit system, with two 24-hour rapid-transit lines. San Francisco has walkable neighborhoods and an OK mass-transit system, but the recent tech boom and ridiculously restrictive development laws have driven the housing prices to an even worse point than New York. Most other eastern cities like DC, Philly, Boston, Pittsburgh, and Baltimore have usable mass-transit systems, along with housing expenses generally correlated with the quality of their job markets.
Some folks are car-free in other significant western cities like Seattle, Portland, Denver and Los Angeles, but it's more of a niche lifestyle most common among young childless folks in a few neighborhoods. Los Angeles, SLC, and Denver seem like they're making the biggest transit investments at present.